Origin of "I'm only three and a half years old"?

Okay, here’s proof – an Abbott and Costello radio show script with “gray” written in playing Matilda, saying the infamous line “I’M ONLY THREE AND A HALF YEARS OLD!” on Page 9:

:setup:

Dude, it’s not been 16 years yet. What is your excuse for not being able to do math?

:waits:

Mahaloth, while I see what you’re trying to do there, it could easily be mistaken as being hostile. I’m sure you didn’t intend that.

I’m almost positive that the phrase originated with Fanny Brice. Fanny Brice played a character named Baby Snooks. The radio show of the same name began in 1933. In addition to the 3 1/2 year old line she also invented “I’ve been a bad little girl.”
Of course Milton Berle always claimed that all the best comedy material was stolen from burlesque and vaudeville.

The Baby Snooks show didn’t air until 1944. Brice first did the character on radio in 1936, and continued it on a bewildering succession of shows before 1942, true, but there’s no indication she ever gave three-and-a-half as the character’s age. Since we have a definite cite for the use of the phrase on Abbott and Costello in 1943 you need more than a bare assertion at this point.

As for the level of jokes in burlesque, read Arnold Auerbach’s memoir Funny Men Don’t Laugh. For his apprenticeship in David Freedman’s radio comedy factory he researched old jokes and got a burlesque comedian to tell him every story he knew. Most of them were unusably awful and that was in the early 1930s.