IanC

Randolph (original and abridged editions) gives us little info on the history. Hastily, I went to Jackson's books. In White Spirituals in the Southern Uplands (1933; Dover, 1965, pp. 173-174), Jackson's version is "Go Tell Aunt Tabby" (incidentally, he doesn't mention the name "Rhody"), saying:

Another favorite type is "Go Tell Aunt Tabby" (Aunt Nancy, etc.). Everybody in the South, singer and non-singer alike, seems to know this tune:

Go tell Aunt Tabby, go tell Aunt Tabby,
Go tell Aunt Tabby the old grey goose is dead.

The one she was saving, the one she was saving,
The one she was saving to make a feather bed.

And according to Jackson's Down-East Spirituals And Others (1943; Da Capo, 1975, pp. 241-242):

The tune is ascribed generally to Jean Jacques Rousseau. This source assumption has been debated, with Lightwood on the negative, and Metcalf and McCutchen on the affirmative side. If one examines the antecedent Rousseau melody (reproduced McCutchen) from which the above tune [i.e. "Rousseau's Dream"] is supposed to have been taken, one may see that the noted French author was merely strolling along in those simplest melodic paths which the folk singers, especially the children, like to follow.

I'm not on the affirmative side. But, anyway, this is an interesting story.

Masato