Yes, that's the right poem. It appears in Moffat's book as 'My Home's on the Mountain', subtitled 'Fairy Haunts' and is ascribed to Joseph Fitzgerald. Moffat's note is brief:

'This air, called "Jackson's Morning Brush" has long been a favourite in both Ireland and Scotland. It was evidently composed by Jackson, a musician of last century, who seems to have resided in Ballingarry, barony of Upper Connello, Co. Limerick, and who was celebrated for his skill on the violin and Irish bagpipes, and for the composition of many lively airs. "The Morning Brush" was printed in Edmund Lee's publication of circa 1775, entitled Jackson's Celebrated Irish Tunes; it was also used by Arnold in his opera, The Agreeable Surprise, 1781; Thompson included it in his Country Dances for 1779, and Aird in his Selection, vol. I., 1782. I have taken the song "Fairy Haunts" from Fitzgerald's Old Songs of Old Ireland, London, 1843.'

Alfred Moffat, The Minstrelsy of Ireland: 206 Irish Songs Adapted to their Traditional Airs, Arranged for Voice with Pianoforte Accompaniment, and Supplemented with Historical Notes by Alfred Moffat: Fourth (Enlarged) Edition. London: Augener Edition No. 8928, n.d., pp 148-9. (Moffat's introduction, reprinted from the first edition, is dated 1897; my copy is inscribed 1916.)

There are rather a lot of 'Jackson's' tunes, many credited to the same man mentioned here: see The Fiddler's Companion, http://www.ibiblio.org/fiddlers/JACKSON.htm.