A little flying dog delights its little girl owner. It’s a picture book but I only remember little girl sitting in a big armchair with the dog perched on the back or maybe it was flying. I think the dog looked like a For context, I’m 54 and would have been a little girl when I had this book.
Didn’t read it, but maybe it’s No Flying in the House?
It’s not a picture book, and the girl flies instead of the dog, but the cover sounds exactly like “No Flying in the House” by Betty Brock. Cover: https://images.gr-assets.com/books/1405527696l/22733517.jpg