My wife, a native New Orleanian, grew up learning a variant of this song. Her version is closer to that posted above by GUEST:Neighmond. I can't recall the whole lyric right now, but it had to do with a kid jumping on the bed; after busting his/her head, mother had to:

Call for the doctor
Call for the nurse,
Call for the lady with the alligator purse.

We have been long been unnaturally interested in all kinds of Gator iconography (needless to say), but I never before knew or guessed that the lady with the alligator purse may have been some kind of healer/shaman/traiteur. What a revelation ~ I like it!