The tune for Moore's song is "Gramachree Molly" from a song by George Ogle, published in the London Magazine, Sept. 1774. Strangely enough, the recent 'Sources of Irish Traditional Music', 1998, didn't recognize that "Will ye Go to Flanders" (their #1055) and "Gramachree" (their #1818, and many later copies) were variants of the same tune. [That's not the only identification they missed.]