CAPE CANAVERAL, FLA., DEC. 11 -- The Navy launched a Trident II submarine missile on an eighth consecutive successful test today after delaying the flight a month because of a dispute over the number of unarmed warheads it would carry.

"We had a flawless launch . . . ," a Navy spokesman said.

After the delay, the launch had been rescheduled for Thursday but again was postponed so it would not occur during President Reagan's summit with Soviet leader Mikhail Gorbachev, according to administration officials who requested anonymity.

The two superpower leaders reported making progress toward a treaty that would limit strategic weapons such as the Trident II.

The 44-foot, three-stage missile blasted away from a land launch pad at 8:26 a.m. and hurled a cluster of instrumented, dummy warheads toward an Atlantic Ocean target.

The launch was delayed originally when it was learned in November that the Defense Department planned to test the missile with 12 dummy warheads, two more than usual. Some members of Congress objected, saying that it would touch off a dispute over the future of arms-control negotiations with the Soviet Union.

The administration agreed to delay the launch pending further consultation with Congress, and sources said today's missile did not carry 12 warheads.

Under arms-control treaties, the number of warheads permitted on intercontinental ballistic missiles was based on the number carried in flight tests.

The Navy has always described the Trident II as designed to carry 10 warheads. Defense Department sources have also said, however, that it could carry more and that, when deployed, some missiles would carry as few as eight warheads and others as many as 12.