Hey, I should have looked sooner at Fuld's Book of World-Famous Music. Here's what it says:

The words (of Dunderbeck) appeared in Our Own Boys Songster (New York, NY, 1876), p. 6, under the title "Dunderbeck's Machine," to the "Air-Thomas's Machine." "Dunderbeck's Machine" is there said to be "By Ed. Harrigan," but this might also mean "sung by" Ed. Harrigan... The music and words of "Dunderbeck" appear in Carmina Princetonia...the book was copyrighted May 16, 1894

So, as Q says, this takes us back to at least 1876. Wish I could see the lyrics and tune from that date.
-Joe Offer-