When I first saw this on Google search page results (yes, I did!), I knew I was going to love the Amy Whinehouse's version :) I love Amy. If I'm not mistaken, Ella Fitzgerald sang this song for the first time.
Anywho, did you know, Birdland was a famous jazz club in New York City located at 1678 Broadway at 44th Street. It had previously been the Clique Club where pianist George Shearing, composer of “Lullaby of Birdland,” first played in 1949 with clarinetist Buddy De Franco. Later that year owner Morris Levy renamed the club Birdland in honor of Charlie “Bird” Parker.
Lullaby of birdland whisper low
Kiss me sweet, and we'll go
Flying high in birdland, high in the sky up above
All because we're in love
Source: Jazz Standards Songs and Instrumentals