Jim Bailey as Barbara Streisand on the Carol Burnett Show. Jim Bailey was a late night TV fixture with his spot-on impersonations of Judy Garland, Marilyn Monroe, Phyllis Diller, and Mae West.
(Jim Bailey with Barbara Streisand)
In 1973, he did a Las Vegas show "The Judy and Liza Show" starring alongside the real Liza Minelli. In 1978, he brought his Barbara impersonation to Super Bowl XII. In 1984, he performed at the opening ceremonies at the Sarajevo Winter Olympics.
The first drag queen to make regular appearances on TV was celebrity impersonator TC Jones on the Ed Sullivan show in 1956, but I haven't been able to find much information about Jones outside of newspaper clippings.