This is best know as "Shule Agra/Aroon", and there are versions in DT, but the song may not be Irish at all. There is a short Scots version, "Dicky Macphalion" in C. K. Sharpe's A Ballad Book, 1823.
One of the most characteristic verses occurs in a English broadside ballad of about 1660. This (1/2) verse goes:
I'll sell my Rock and eke my Reel,
And after that my Spinning wheel,
To buy my love a cap of Speel,
And follow my Cavalilly man:
I'le pawn my Kirtle and eke my Gowne,
Which cost my Mother many a Crowne,
And goe with thee from Town to Town,
Then prethee le me gang with thee Man:
In this ballad she does not lament her soldier lad in the Scottish army going off to war, she goes with him. This ballad "The North-country Maid's Resolution, and Love to her sweetheart", (tune, "Cavallily Man") is in The Euing Collection, #257. The English broadside is probably based on a Scots song of the civil wars. A 17th century Scots copy of the tune "Cavallily Man" was called "Roger the Cavalier".
So the original was probably by some Scotsman abround 1645, but it has been reworkred several times since.
For some notes on Irish versions see Donal O'Sullivan's edition of the Bunting MSS in 'The Journal of the Irish Folk Song Society'. 1927-39.