It is interesting that the Traditional Ballad Index researcher speculates that 'Johnny, Fill Up the Bowl', which shares the tune, probably came first. Patrick S. Gilmore (the 'll' in the quote below is probably a typo) was the real name for Louis Lambert, given as author of 'When Johnny Comes Marching Home':
Scholars continue to argue whether "When Johnny Comes Marching Home" or the doleful "Johnny, I Hardly Knew Ye" is the original. "When Johnny Comes Marching Home" can be firmly dated to the beginning of the Civil War, while "Johnny, I Hardly Knew Ye" does not appear until slightly later (1869) -- but as a traditional song. The earliest known printing is, in fact, that of "Johnny Fill Up the Bowl" (early 1863). If I were to make a guess, I think I would put "Johnny Fill Up the Bowl" first; it's a logical tune for Gillmore to steal (and some anonymous Irishman to turn into an anti-war song). But what do I know? - RBWCheers, Stewie.