I just posted this on the Advent & Development thread and I want to post it here as well since it follows up on Gibb's two posts above.
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Here is another reference to "going to Georgia", which introduces the "Jenny gone away" song as well. The line is

"Oh! my massa told me, there's no grass in Georgia."

"Upon inquiring the meaning of which, I was told it was supposed to be the lamentation of a slave from one of the more northerly states, Virginia or Carolina, where the labor of hoeing the weeds, or grass as they call it, is not nearly so severe as here, in the rice and cotton lands of Georgia. Another very pretty and pathethic tune began with words that seemed to promise something sentimental -

    "Fare you well, and good-by, oh, oh!
    I'm goin' away to leave you, oh, oh!"

http://books.google.com/books?id=WaFiAAAAMAAJ&pg=PA128&dq=Jenny+gone+away&cd=2#v=onepage&q=Jenny%20gone%20away&f=false

This is from JOURNAL OF A RESIDENCE ON A GEORGIAN PLANTATION IN 1838-1839, by Fanny Kemble.