It is indeed a music-hall song. As catalogued:

OH! MOLLY MCINTYRE (I'LL BE A SCOTCHMAN FOR YOU)
Words and music by Fred Godfrey and Billy Williams ; sung by Billy Williams.
London : Francis, Day & Hunter, ©1913.

First line: Patrick Malone from County Tyrone.
First line of chorus: Oh! Molly McIntyre.

More information:
http://www.fredgodfreysongs.ca/Songs/Oh_Molly_McIntyre.htm

There's a recording on YouTube.

I can't find any sheet music images online, but I might be able to transcribe it from the recording. Keep watching this thread.