Also verse similarities with "Sally, git your hoe cake done."
This little rhyme has a similar meter as well:

REDHEAD WOODPECKER

Redhead woodpecker; "Chip! Chip! Chee!"
Promise dat he'll marry me.
Whar shall de weddin' supper be?
Down in de lot, in a rotten holler tree.
What will de weddin' supper be?
A liddle green worm an' a bumblebee,
Way down yonder on de holler tree.
De redhead woodpecker, "Chip! Chip! Chee!"

T. W. Talley, 1991 rev. ed, Negro Folk Rhymes, no. 275.
Some of these rhymes come out of old minstrel songs.