When one thinks of Australia, the first thing that comes to mind is not necessarily prowess in the arts. Kangaroos, koalas, brawling outbackers, sprawling sheep stations and a thousand miles of railroad spanning a vast expanse of red desert are the more usual mental images.

Yet this small society of 16 million on a water-locked continent has a flourishing arts life, centered in the great coastal cities and closely wired into the contemporary world scene, as those who toured there recently with the Mormon Tabernacle Choir found out.Of course Australia has had considerable arts for a century or more. Some of opera's grandest dames - Nellie Melba, Marjorie Lawrence and Joan Sutherland - came from there, and visiting attractions have always toured.

But the cornerstone of Australia's musical arts was decisively laid soon after World War II, with the founding of symphony orchestras by the Australian Broadcasting Corp., which sponsored the choir's tour.

There are now six such symphonies - in Sydney, Melbourne, Adelaide, Perth, Brisbane and Hobart, Tasmania. Their official booking office is in Sydney, and they tend to rotate an international soloist or guest conductor through several orchestras. The Australian Chamber Orchestra and other independent groups bring the number of Australian orchestras to 12.

Great orchestras need homes, and the great halls of Australia, all constructed within the last 20 years, have served as both headquarters and catalysts to further arts activity. And since all the large cities of Australia are coastal cities, located at the mouths of rivers, they provide striking sites for arts venues.

Between the two largest cities of the continent - Sydney with 3.3 million inhabitants and Melbourne with 2.8 million - there exists a sharp rivalry, with much good-humored bantering. "Yes, Sydney is such a nice place," said the Melbourne taxi driver, "it's a pity they had to build it so far out of town!"

A lady who frequents both cities summed up the difference in their arts facilities. "The Melbourne complex has stressed the beauty within, and the halls are superb. In Sidney, the exterior is the most striking feature."

Striking is only a beginning of the adjectives to describe one of the world's great buildings, an architectural wonder and probably the most beautiful arts center exterior anywhere.

Situated on historic Bennelong Point, a stone's throw from the bustling circular quay on Sydney Cove, the Sydney Opera House takes the

breath of even those who think they are prepared for its effect. After innumerable construction headaches and expense overruns, it seems a fanciful outgrowth of its site - its billowing sails cast in concrete, its tiled roofs catching daylight sun and night illumination in a pearly, roseate glow.

A Dane gave Sydney its opera house (though it houses all the arts, it is never known otherwise) when in 1957 Jorn Utzon, then 38 and little experienced, won an international contest. Inspiration sprang from his experiences as a child living near seaside Helsingoer (Elsinore of "Hamlet" fame), where the castle caught his fancy of how a big building should look, placed at the water's edge.

With Ove Arup and Partners as consulting engineers, the thorny problem of how to construct and support the vaults (not shells) was undertaken. A genius geometrician, Utzon himself came up with the solution of precasting the roof - making small curved shapes on only 10 different molds, then gluing them together and covering with special Swedish ceramic tile. It is said the idea came to him while peeling an orange.

Utzon resigned in 1966, and the interiors may have worked out more gracefully had he remained. Backstage space is nonexistent in the concert hall, and scenery designed to operate vertically doesn't necessarily work well. Nonetheless, there are nearly 1,000 rooms in the complex, including the concert hall (2,690 seats), the opera theater (1,547 seats) and three smaller theaters. Decor is striking, acoustics good and foyer areas spectacular, especially those behind the halls, that look out through glass walls over Sydney Harbor.

In Melbourne an arts complex was first proposed in 1944, across from the Alexandra Gardens and on the bank of the Yarra River. The plan grew to fruition through the genius of one commissioned architect - Sir Roy Grounds.

After years of dreams and struggle, the beautiful buildings of the Victorian Arts Center have taken their places one by one: the National Gallery (1968), the circular concert hall seating 2,677 (1982), and the three theaters, under a beacon white spire designed to simulate a ballerina's spreading skirt (1984). The Myer Music Bowl, dating to 1959, seats 5,000 for many outdoor events.

Creature comforts abound and harmonious vistas pamper the eye in this stunning complex, with luxurious foyers of carpet, glass and brass and a fabulous art collection. Decor is cued to colors of the Australian landscape, its mineral wealth, precious and semi-precious stones.

Walls of the concert hall, painted in subtle strata of coral, sand, lavender and gray, are a work of art in themselves, and the sound is superb. This hall, like all others in Australia, features a fine concert pipe organ.

Adelaide, capital of South Australia, is an arts-conscious city whose energies center around the ambitious Biennial Arts Festival, with a wide-ranging format like the Edinburgh Festival. The city opened its Festival Center in the early '70s - a gleaming white, winged complex that includes a concert and opera hall, a playhouse, an experimental theater and outdoor amphitheater.

Perth's attractive concert hall is constructed in the classic colonnaded Grecian style. This beautiful city on the Indian Ocean is noted for its thriving Ballet of Western Australia. Indeed, the country has about 15 ballet or dance troupes, most important being Melbourne's Australian Ballet, which is now touring Russia. The Sydney Dance Company reflects the country's interest in contemporary dance.

The Queensland Cultural Center in Brisbane, located on the Brisbane River right next to Expo '88, is playing host to many arts offerings of the Exposition this summer and fall.

The magnificent new concert hall, opened in 1984, seats nearly 2,000. Beautifully decorated in warm earth tones, its sound is among the country's finest. Also on site are the equally large Lyric Theater, the intimate Cremorne theater, and the state art gallery, museum and library.

The Queensland Museum has assembled an exciting exhibit of Aboriginal art from many sources, representations of that people's "dreamings," or myths, in painting and carving. Significant museums throughout the country quite rightly concentrate on Aboriginal and Polynesian aspects, and original Australian painting. However, there are surprising pockets of traditional art. For example, the Melbourne Museum has hundreds of Rembrandt pen sketches - the most I have ever seen in one place.

How would American arts like to have a third of their expenses paid by government? Not the full amount, mind you, as in some European countries, but certainly a lot more than the skimpy 12 to 13 percent that U.S. federal and local government comes up with.

That's the proportion that Australian governments provide for their arts, according to Justin McDonnell, a freelance consultant to the arts in Australia. Funds are administered through the Australia Council, which corresponds to our National Endowment for the Arts, "but people here have regional pride, and the arts organizations tend to paddle their own canoes," said McDonnell.

However, cooperation brings international music to isolated Australia. For example Musica Viva, the largest chamber music impresario in the world, annually presents more than 2,000 visiting artist events.

Largest of the country's five opera companies is the Australian Opera in Sydney, which maintains a resident company of some 40 singers, supplemented by international stars such as Leona Mitchell and James Morris. It plays a winter season of 22 weeks, and in summer about nine weeks.

Two performances demonstrated its scope. "The Rake's Progress" by Stravinsky, in an attractive staging that combined mannered Georgian England with a modern raffish look, had international tenor Neil Rosenshein as the ill-fated Tom Rakewell.

Also playing was Massenet's "Manon," expertly clothed in 18th-century French charm. Glenys Fowles in the title role typified the sort of healthy, well-trained, pretty singer this land seems to produce. Staging, musical preparation, orchestra (the Elizabethan Philharmonic), an excellent chorus and good conducting left the impression that the Australian Opera is a tight ship, well run in its own theater under the arches of the Sydney Opera House.

In addition, the Victorian State Opera in Melbourne imports singers and does 50-60 performances a year. The three other state companies - Lyric Opera of Queensland based in Brisbane, South Australia Opera in Adelaide and Western Australia Opera in Perth - each do four or five productions annually.

Musical education, like all other education in Australia, infant to Ph.D., is totally funded by the state. Before entering one of the state conservatories a student must pass a demanding test, and entry is limited by the number of possible slots, but a talented student can go far, said McDonnell. The same is true of dance and acting, and talent in Australia has proliferated under this system as conservatories have grown up since World War II.

Myer Fredman, now in Salt Lake City to direct the International Summer Vocal School, heads the opera school at the New South Wales Conservatory of Music in Sydney. He agreed that the conservatory system has produced "national treasures" of music, with about 85 percent of graduates going on into the profession.

During the past 20 years, McDonnell has observed two exciting trends toward the "Australianization" of the arts.

"First, beginning in the '60s we have had an explosion of writing, principally for the stage. Our own young writers have put Australia on the stage, and we hear our own accent, where before you never heard anything but a British accent." (In June at Sydney Opera House one could see "Dinkum Assorted" by Linda Aronson, about women working in a biscuit factory during WWII.)

"Secondly, our film industry has taken off, and many of our pictures are seen in the U.S. and around the world."

Fredman conducted for the Royal Philharmonic and London Philharmonic, and spent 15 years at Glyndebourne before going to Australia in 1974. He spent six years with South Australia Opera in Adelaide before moving to Sydney, where he sometimes conducts the opera.

"Our greatest problem is the `tyranny of distance,' and the danger of becoming complacent, without pressing competition," he said. "But the future is very encouraging, there is a surge of vitality; the most important thing is to sow the seeds of accomplishment in the young."