Here is a reference to a rowing song from Fanny Kemble's JOURNAL OF A RESIDENCE ON A GEORGIA PLANTATION IN 1838-1839:

http://books.google.com/books?id=w34FAAAAQAAJ&pg=PA128&dq=%22Jenny+gone+away&cd=3#v=onepage&q=%22Jenny%20gone%20away&f=false

The setting is a boat trip across the Altamaha River from the Georgia coast to the St. Simon's island. Kemble gives a detailed description of the boat, the process of rowing and of the singing, and offers these words:

"Jenny shake her toe at me,
   Jenny gone away;
Jenny shake her toe at me,
   Jenny gone away.
Hurrah! Miss Susy, oh!
   Jenny gone away;
Hurrah! Miss Susy, oh!
   Jenny gone away."

A bit further on she quotes a fragment from another song:

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

The "Jenny gone away" reminds me of the song "Ginny's Gone to Ohio". Here is another reference to the "Jenny" song from a little later (sorry to jump the gun a bit) in 1843, on the occasion of a corn-shucking. Here you have a good description of a "corn-shucking shantyman"! (my label) :

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

And here's a footnote about the reference to Jenny "shaking her toe":

http://books.google.com/books?id=bFLiWrJo5_MC&pg=PA261&dq=Jenny+gone+away&lr=&cd=11#v=onepage&q=Jenny%20gone%20away&f=false