The song belongs with the version (or similar) given by Bruce Olson in thread 47949, from Herd's Scotch Songs, 1776: Will ze go to the wood Fozie Mozie
Olson says the song given there is without title. He included Lyr. Add. in his post, but the song has not been collected.

Malcolm Douglas and McGrath of Harlow (same thread) have provided information on other old versions, which seem to have been widespread in the British Isles.