I think we can push this song back even earlier! I've found a reference in The Life of Robert Edward Lee (by H E Shepard, 1906) to civil war soldiers singing:

He that has good whiskey,
And giveth his neighbor none,
He shall have none of my good whiskey,
When his good whiskey is gone.

Also, a contemporary letter of Mark Twain (1863) from Carson City, Nevada refers to someone singing "the pea-nut song." It could be another pea-nut song, true, but the footnotes to Early Tales & Sketches, Vol. 1: 1851-1864 identify it as the "Good Peanuts" song.