This was one of a number of whimsical "novelty songs" popular during the 1930's and 1940's in the U.S. Most musical groups had one or two in their act. Some acts lived off them.

Some of the others I can recall are:
"Mairzy Doats"
"The Merry Go Round Broke Down" (theme song for Warner Bros.
                                 Cartoons)
"Open the Door Richard"
"The Boogie Woogie Bugle Boy of Company B"
"I Like Bananas"
"I've Got a Lovely Bunch of Coconuts"
"Yes, We Have No Bananas"
"Nellie, the Nudist Queen"
"Der Fuhrer's Face" (and almost anything else by Spike Jones)
"Lydia, The Tattooed Lady"