There's a rhyme that's similar to this one called 1, 2, 3, 4, 5, Once I Caught a Fish Alive.

1, 2, 3, 4, 5, I Caught a Hare Alive - English Children's Songs - England - Mama Lisa's World: Children's Songs and Rhymes from Around the World - Intro Image
1, 2, 3, 4, 5, I Caught a Hare Alive - English Children's Songs - England - Mama Lisa's World: Children's Songs and Rhymes from Around the World - Comment After Song Image
1, 2, 3, 4, 5, I Caught a Hare Alive - English Children's Songs - England - Mama Lisa's World: Children's Songs and Rhymes from Around the World 1
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Thanks and Acknowledgements

This rhyme can be found in A History of Nursery Rhymes (1899) by Percy B. Green. The 1st illustration is from Mother Goose, The Original Volland Edition (1915), edited and arranged by Eulalie Osgood Grover and illustrated by Frederick Richardson (with some graphical editing by Mama Lisa). The 2nd illustration is from The Real Mother Goose (1916), illustrated by Blanche Fisher Wright. The 3rd illustration is from Traditional Nursery Songs of England with Pictures by Eminent Modern Artists edited by Felix Summerly (1843).