Version from Beth's Music Notes. She cites Ruth Crawford Seeger's book American Folk Songs for Children in Home, School and Nursery School : a Book for Children, Parents and Teachers. That version has the major version of the melody.
Herbert Halpert was a folklorist. I found a recording of his that is titled "Old Uncle Rabbit" from Mississippi.
I attempted to access more of Herbert Halpert's recordings, but the Library of Congress links were not working.