A moppet is a rag doll.

I Had a Little Moppet - English Children's Songs - England - Mama Lisa's World: Children's Songs and Rhymes from Around the World - Intro Image

Notes

*A rag doll

Thanks and Acknowledgements

This rhyme can be found in A History of Nursery Rhymes (1899) by Percy B. Green. The illustration can be found in The Real Mother Goose (1916), illustrated by Blanche Fisher Wright.