The same tune pops up throughout "Dog Tired" with the curious pups (also 1942). It later shows up in McKimson's "Muscle Tussle" (1952) during the scene where the huckster swindles Daffy into taking a "free" sample of 'Atomcal' elixir. Well, the all-knowing Jerry Beck informed me that the title of song was Louis Prima's "Tica Ti Tica Ta". Poking around on Google I found it was recorded by the likes of the Andrews Sisters, among others. I also dug up this YouTube video featuring a version of the song performed by Ginger Harmon and the Mercer Brothers.
It's funny that the song has NOTHING to do with the scenes that Stalling used it in (involving fixing breakfast or a con man on the beach), yet it fits perfectly anyway. That's the genius of Carl Stalling for ya.