The children's song in DT is much older than the source cited there. Wm. Stenhouse gave it, calling it an old 'nursery ditty', in 'Illustrations to the Scots Musical Musuem', #237, and said that it was the original from which Allan Ramsay borrowed a line or two. SMM #237 is Allan Ramsay's song, but set to the tune "Deil Stick the Minister", rather than "This is no my ain house". Both tunes are 17th century ones.

The Jacobite song is given in James Hogg's 'Jacobite Relics', I, #37, 1819, but is given rather curiously, with chorus first (O this is no my ain house) and then 1st first verse (A carle came wi' lack o' grace) set to music, after which are printed the rest of the verses, with the chorus noted to be sung after each verse.

I suspect the Jacobite song was one of Hogg's own. Hogg in his notes said "...; but I really expect that the publication of these Jacobite relics will work a revolution in Scottish song, and that, for a time, we shall hear them more generally sung than any other." If the song were known earlier, then it seems that 'revolution in Scottish song' would have already past.