In addition to Rikki-Tikki-Tavi, Rudyard Kipling wrote a lot of other animal stories including The Jungle Book (just say no to Disney!) and the whole series of "Just So" stories that explain in fanciful ways how animals received their various physical features.
Cleveland Amory has written numerous books about cats such as The Best Cat Ever and The Cat Who Came for Christmas. Personally, though, I prefer the "Cat Who..." series of mystery books by Lillian Jackson Braun (I hope I'm spelling that right), which pairs Siamese cats with a crusty old journalist. (By the way, her books portray journalists more accurately than any other books, TV shows, or movies I've ever encountered.)
Oh, and please don't discount books like Watership Down or The Wind in the Willows. They're so beautifully crafted that I don't think it's fair to categorize them as children's books. Good literature has no upper age limit.