The Pentagon, struggling to keep military doctors from quitting for better money elsewhere, soon will establish a hefty bonus system under which some surgeons could earn $112,250 a year while in uniform.

Under the program, which takes effect Jan. 1, physicians with critical skills now in short supply - such as surgeons - can boost their salaries by up to $20,000 a year if they agree to re-enlist for four years.Smaller "retention bonuses" will be paid to physicians who re-enlist for two or three years.

A surgeon who signs up for another four-year hitch under the program would see his total monetary compensation rise from roughly $92,250 a year to $112,250 a year.

"The Department of Defense and the Congress believe we have spotted a problem here in time to do something about it," says David Newhall, the No. 2 executive in the Pentagon's health affairs office. "There are other severe non-salary problems that contribute to the loss of military physicians, but this is a key start."

Congress authorized the new bonus program in the Pentagon's fiscal 1989 budget and earmarked $30 million for the effort as long as the Defense Department meets certain requirements.

The most important was a report to Congress by Nov. 15 comparing military and civilian salaries along with a plan for divvying up the money among different types of physicians.

Another report focusing on military health professionals other than doctors is due by Dec. 1.

Newhall said the Pentagon met the Nov. 15 deadline for the first report and will meet the deadline for the second.