The tune is traditional, almost certainly taken by Fr O'Neill from the very popular "Moorlough Shore". The origins of this song and the location of "Moorlough" or "moor lough" are uncertain but generally taken to be Moorlough Bay on the north Antrim coast, not a million miles from Portglenone where Fr O'Neill was born and raised. There was a very scholarly thread on "Moorlough Shore", last year I think.

Mrs Milligan-Fox was a sister of Alice Milligan, poet and patriot (1866-1953). It's just struck me that she was born in the same year as Mary Anne McCracken died - makes 1798 seem not all that far away!