Brian Dowling, the former Yale quarterback and the inspiration for a Doonesbury comic strip character, has signed with the Washington Redskins.

Dowling, 30, has been out of the National Football League since 1973, when he was listed on the roster of the New England Patriots but did not throw a pass.

The Redskins also signed another Patriot reject - defensive end Perry Brooks, a 6-foot-4, 260-pounder who was a sixth-round draft choice last year before being released.

"Perry could be a real sleeper," said Bobby Mitchell, the Redskins director or pro scouting. "He's got tremendous possibilities as a pass rusher, which we need. The Patriots just didn't give him any time. We can."

Dowling is the first quarterback free agent signed by the Redskins this offseason. He and Brooks participated yesterday in one of George Allen's workouts before the preseason for assorted veterans and free agents at Redskin Park.

Dowling becomes the third quarterback on the Redskins' roster, joining Billy Kilmer and Joe Theismann. The Redskins' third quarterback of a year ago, Randy Johnson, was released in midseason.

With the new squad size at 43 players and a two-man taxi squad, the Redskins most likely will keep three quarterbacks this season.

Dowling is known to millions of comic-section devotees as B. D. in Doonesbury, the strip penned by his former Yale classmate Garry Trudeau.

Dowling and Redskin running back Calvin Hill entered Yale at the same time, both as freshmen quarterbacks. Hill was switched to running back and became a No. 1 draft pick.

Dowling starred at quarterback for Yale and was an 11th-round draft choice of the Vikings in 1969. He was cut that year, played in the minor leagues and was signed by the Patriots in 1970.

He spent two years on the New England taxi squad, completed 29 of 54 passes for 383 yards and two touchdowns in 1972 and left to join the WFL in 1974. He played with New York and Charlotte franchises for two years, and did not play last season after trying out in the Candian League.