Yes, that's the text in the DT at The Deserter, though you do give correctly the word "six" in the final verse, which somebody with a tin ear has put in the DT as "sticks". No need to quote the whole thing, though; a simple link would have sufficed.

The song was still quite widespread when collectors were out looking for songs at the beginning of the 20th century; most examples were found in England, with some in Scotland too. The Roud Folk Song Index lists many of these at number 493; at present none, so far as I can see, from Ireland. If the tune came from Luke Kelly, I've no idea where he got it, or whether it belonged to this song or to another.

As for "much older": not really. It certainly pre-dates Albert, but probably not by a great deal. See, for example, a number of broadside editions at Bodleian Library Broadside Ballads:

The new deserter

Some name Albert (the later ones include Ratcliffe Highway), others, only a few years earlier, name (a) Duke of York.