Come to think of it there is some affinity with the tune of the older song 'Long grey beard a wagging'/The Old Man from Lee' Roud 362. The oldest version I have goes back to 1730, but may be older.

The 1730 version in The Musical Miscellany has its tune but I don't read music well enough to say that recent versions are related. Early versions are all Scottish and closely related, though it seems to have become quite widespread in Britain and America early on in anglicised forms.

THE YOUNG LASS CONTRA AULD MAN

The Carle he came o'er the Craft,
And his beard new shav'n,
Glow'rd at me's gin he'd bin daft,
The Carle trows that I'll ha'e him,
Hows awa' I wonna ha'e him,
Na forsooth I'll no ha'e him!
New hose, new shoon,
And his Beard new shav'n.

(3 more stanzas)