If you owned this book in the 50's you may be confusing to books with similar little girls. Both looked like Little Golden books but were Ding Dong School Books.
Debbie and Her Nap and the other title is Daddy's Birthday Cake. In Daddy's Birthday Cake the little Girls name is Linda and she bakes a cake with her mother.
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Looking for a book that I remember was about a little girl named Debbie baking a cake.