I couldn't find this rhyme in some of the most comprehensive collections of nursery rhymes (like The Oxford Dictionary of Nursery Rhymes and The Annotated Mother Goose). Perhaps it was new to the early 20th century.

I found it in The Little Mother Goose (1912), illustrated by Jessie Willcox Smith, and printed in the USA. It can also be found in Primer Language Reader Series (1909), by Franklin T. Baker, and printed in New York.

If anyone knows anything about the origin of this rhyme, or if you recall hearing it growing up, please email me and let me know. -Mama Lisa