Here is "Jenny gone away" at a corn-shucking, from 1843, in THE FAMILY MAGAZINE, from an article entitled "Visit to a Negro Cabin" "(Extract from a Journal, kept by a Gentleman, who travelled through Virginia some years since.)".   

"Oh, Jenny gone to New-town,
   Chorus: Oh, Jenny gone away!
She went because she wouldn't stay,
   Oh, Jenny gone away!
She run'd away, an' I know why,
   Oh, Jenny gone away!
For she went a'ter Jone's Bob.
   Oh, Jenny! &c.
Mr. Norton, good ole man,
   Oh! &c.
Treats his niggers mighty well.
   Oh! &c.
Young Tim Barnet no great thing....
Never say, come take a dram....
Master gi's us plenty meat,...
Mighty apt to fo'git de drink....

http://books.google.com/books?id=cYAAAAAAYAAJ&pg=PA244&dq=Jenny+gone+away&cd=6#v=onepage&q=Jenny%20gone%20away&f=false