When my oldest daughter was very young, in the early 1980's, her favorite book was But Not the Hippopotamus by Sandra Boynton. I think we all still have this book committed to memory! It's the delightful story of a hippopotamus who wouldn't participate in anything until the other animals asked her to join them. (With a wonderful little surprise at the very end.) I couldn't help but think of it when said daughter's rat was on the ottoman next to our cat--minus any running hats.