There is an old thread on this which I guess Malcolm Douglas can find. The source Lady John Scott's boy singer used is traceable - it's a broadside of 1820 by John Sanderson of Edinburgh, one of several British broadside-mongers to call their business "The Poet's Box". If somebody gives me a round tuit I can go find it, there are two obvious places to look.

Given its content and style there is no way the Irish song can be earlier than Sanderson. The tune was published by Nathaniel Gow in 1819, which is presumably how it came to Sanderson's attention.