This is only a guess, but I think it's an original piece of music, in the style of a 30s swingin' big band.
It's getting more and more expensive to license music for film and TV. Not only do you have to pay the publisher, but licensing fees for the original recording if you wish to use it. Sadly, very little of that money goes to the writers and performers of some of this music, which is why Brian has spent some time in the studio in recent years re-recording some of his more popular songs for licensing in various forms of media, like commercials, film, and TV.
Some shows, especially animated ones like Family Guy, American Dad, and the Simpsons, where music plays a rather important role, (and where the production budgets are much smaller than live-action shows) use a gifted music staff to score their episodes, and pride themselves in using all original music. Family Guy and American Dad very often use a big band for much of their music, and one drummer who features prominently in the music for these two shows is Bernie Dresel. It sure sounds like it could be Bernie on this episode.
Tele-billy