This is a poor shadow of thread 13537, the Origins thread, where several theories are discussed, some with partially supporting evidence. That the song is old (c. mid-19th C or so), most agree; the earliest date is 1909 (Perrow) although an 1875 Saturday Evening Post article has been mentioned.
Most consider it to be of Black origin.

The version collected by Scarborough (printed 1925) with brief score is one of the best, superior to the one in the DT.
It has a great many variations, as would be expected of an old dance-play song.

I doubt that any story of its origin will be agreed upon by those who have tried to trace its history.