Interestingly enough, this old minstrel song, "My Mary Ann" is one I can document as being in California in 1854, which is where it was published, and in Port Phillips Head, Australia in 1851, being used as a rowing/pumping song. Here is the account from William Craig in his book MY ADVENTURES ON THE AUSTRALIAN GOLD FIELDS (1903), referring to events in 1851:

http://books.google.com/books?id=sIoDAAAAYAAJ&pg=PA8&dq=%22Oh,+fare+you+well,+my+own+Mary+Ann,&lr=&cd=1#v=onepage&q=%22Oh%2C%20f

And here is the sheet music information on "My Mary Ann":

https://sherlock.ischool.berkeley.edu/cgi-bin/CSMPSearch2.tcl?CSMP@docid+1279

I'm not sure how Mr. Craig could have been singing this song in 1851 if it hadn't been published until 1854. Perhaps there were earlier versions of it out there. I haven't been able to find any earlier publication dates. Mr. Craig is looking back at least 50 years in his memory here.