I should have quoted the opening so you could judge whether this is the same song.

Kathleen Mavourneen! the grey dawn is breaking,
The horn of the hunter is heard on the hill

The book I noted is one I picked up a few years ago, a decrepit copy, for $5 in a used book store, so it's not a rare one.

Mrs. Johnson gives a history of song and tune, and mentions a sequel called "Dermot Ashtore".