A book I love that fits this description is Understood Betsy, an old-fashioned historical novel that works with younger readers. Fantasy can also be both challenging enough and emotionally suitable. Animal fantasies like Poppy by Avi, which is the first book in a series, are written for older children, but there is no reason why your daughter would not enjoy them. Nonfiction is also good, if she has subjects she is interested in. The sky's the limit.
Nursery rhymes are excellent.
A good Mother Goose collection is a great book to have around the house. My First Mother Goose by Iona Opie is a good choice. Board books are also good. They are made of heavy cardboard, so they're durable. There are excellent board books with primary colors and just a few, well-chosen words.