BMI.com lists 152 songs by Jimmy Driftwood, but none of them is called PUPPY IN THE BOTTOM OF THE POT. In fact, I couldn't find even one of his songs that had any of the words PUPPY, BOTTOM, or POT in the title.

This Jimmy Driftwood discography doesn't have it either. Neither does Allmusic.com.

If you Google for "puppy in the bottom of the pot" the only thing you find is this thread.