Galvin's "1798" version given above by Bob Coltmanis is described as "The old street ballad of 1798" in "The Career of Dion Boucicault," by Townsend Walsh (1915), p. 193. Walsh also prints Boucicault's rewrite.

But Walsh doesn't explain his confidence in the 1798 date.

Redfern Mason, "The Song Lore of Ireland" (1911), p. 309, also attributes the song's origin to 1798 and quotes a stanza about Bonaparte, but he is likewise mum on the source of his dating.

My suspicion is that "1798" is just an educated guess based upon the presumed topicality of the words.