That's Scottish, not Irish, Gaelic! Mò Rùn Geal Òg has been discussed here in the past, briefly, and a few verses of it posted. The Chisholm story is anecdotal and should not be quoted as fact (it isn't the only ascription), though it may be true.

Where did you get your text? Not directly from the Mod collection, as you state on your website. Perhaps from another website? Various texts are quoted all over the place, it seems, mainly from recordings by Capercaillie and by Maggie MacInnes and her mother Flora MacDonald. So far as I remember, Capercaillie and Maggie got the melody from Flora, and it isn't easily recognisable in the transcription on your site;it certainly fooled me, anyway. Where did you get it? Not directly from Fraser (as your site implies), or you wouldn't have needed to ask questions about it. It really is important to be accurate. If you have the material from secondary sources, say so; after all, they may not be correct transcriptions from the sources they name, and I'm sure you wouldn't want inadvertently to mislead people.

John Lorne Campbell (Gaelic Folksongs from the Isle of Barra, Linguaphone Institute / Folklore Institute of Scotland, n.d., p 49; notes, Mò Rùn Geal Òg) observes:

"Very unsatisfactory versions of the air have been printed in the collections of Highland music published by Patrick MacDonald (1781) and Simon Fraser (1816 and 1874), the editors having been completely confused by the changes of time signature which take place in the tune."

That would seem to confirm that you've found the song you were looking for, anyway; though you don't have the best tune for it. The Campbell pamphlet, incidentally, accompanied a sound recording (which I don't have) so contains only Gaelic lyrics, translations into English, and notes; no music transcriptions.