Fairy Tale, Fable
As an adorable children's book, The Velveteen Rabbit straddles the line between fable and fairy tale. It's like a fable because it has all kinds of useful truths and lessons to impart (about life and love and what exactly it means to be "real.")
It also fits into the category of fairy tale because it features magic and fairies—literally. There are talking toys and animals and a fairy who comes and turns a stuffed animal into a real rabbit.
Watch out, Cinderella. You don't get much more enchanted than that.