There's a fairly obscure song known as "Rabbit Hash" also in the African-American tradition.

Her's a field recordings of an African-American verion that is very similar:

Field Recordings Vol. 8: Louisiana, Alabama, Mississippi (1934-1947)

Rabbit, rabbit siftin' in the sand
I wish I had him in my hand

Oh rabbit hops, Oh rabbit skips,
Oh rabbit hop right in my pot