The onsite search engine (see "Lyrics and Knowledge Search" box at the top of every page) finds several references to published examples, and one file in the DT:

The Tailor and the Mouse

That one is taken from the Burl Ives Song Book; no previous source is indicated for text or tune. Another, slightly longer example (tune very close) was printed in Sabine Baring-Gould and Cecil Sharp, English Folk-Songs for Schools, 1905; it seems to have been collected by Baring-Gould. Apparently derivative of The Tailor and the Louse, which has been discussed here in the past.