A You're Adorable (The Alphabet Song) was a standard popular song, not exactly jazzy though. You can see the sheet music at the Levy Collection. It's under copyright so I can't link you to the sheet music images, but you can see it in a pdf file there. Rather than link you directly to the pdf, I'll point you to the search page: Levy Search; if you put adorable in the first search box and search the song will be the first one you get. You can download the pdf from there, or look at it online if you want.

Mick