Hi, GM5!
Some picture books (generally below her reading level, though) with nice illustrations, animals as central characters, not sad or scary, and some funny...I hope some of these might appeal:
Chris Wormell, Henry and the Fox, George and the Dragon, Two Frogs (brilliant illustrations, easy text, peerlessly funny)
James Marshall, George and Martha books, Fox books (easy readers, very witty)
Barbara Reid, The Subway Mouse (really interesting plasticine illustrations--nice sweet little story about taking risks to make a better life for oneself); also The Golden Goose, and The Party (no animals in this one, though)
Jon Muth, Zen Shorts, Zen Ties, The Three Questions (reinterpretations for children of classic Buddhist tales, haiku form, and a Tolstoy story, respectively; nice watercolour illustrations; good for the thoughtful child)
David Wiesner, The Three Little Pigs (self-referential telling of the classic; hilarious and clever); also Tuesday has animal protagonists
Mary Azarian, Barn Cat (a counting book, but with gorgeous woodcuts--worth it for the pictures!)
Tim Wynne-Jones and Eric Beddows, Zoom at Sea, Zoom Away, Zoom Upstream (delicate pencil drawings, exciting and rather surreal adventures of an intrepid cat, in search of his missing uncle)
Paul Owen Lewis, Storm Boy, Frog Girl (two quite similar tales drawn from Kwa'kwa'ka'wakw themes of the relationship of humans to animals, and our responsibilities to the natural world)
Helen Cooper, Tatty Ratty (adventures of a toy rabbit, gone missing from his little girl--gorgeous pictures); Pumpkin Soup (three animal friends quarrel and make up; again, brilliantly imaginative illustrations)
Marjorie Flack, Angus and the Cat, Angus and the Ducks, Angus Lost (really for quite little ones, but very funny--good at bedtime)
Munro Leaf and Robert Lawson, Ferdinand the Bull (a classic, with a great message about being true to oneself)
Ezra Jack Keats, Whistle for Willie, Pet Show, Hey Cat, Over in the Meadow (again really for littles, but sweet--I love the open-endedness of the stories and the textured feeling of the illustrations)
Julia Donaldson and Axel Scheffler, The Gruffalo, The Snail and the Whale, Room on the Broom, Charlie Cook's Favourite Book, et al (these two are an industry, but the books are very clever and lots of fun)
Beatrix Potter's books of course are so beautiful, and a nice little size for small hands; the text in several of them is actually very advanced (The Tailor of Gloucester, for instance)
Kenneth Grahame, The Reluctant Dragon (not to be missed!)
Some chapter books with several pictures and animals as central characters (and much closer to her real reading level than the picture books I mentioned) that I can think of include a lot of the classics:
-EB White's Charlotte's Web, Stuart Little, Trumpet of the Swan;
-CS Lewis's The Lion, the Witch, and the Wardrobe--a bit too scary at the end?--The Horse and his Boy is less scary, I'd say;
-Sheila Burnford's The Incredible Journey;
-Kenneth Grahame's The Wind in the Willows;
-not enough pictures, probably, but TH White's The Sword in the Stone is completely brilliant--much harder than 4th, though--a good read-aloud?;
-Carolyn Sherwin Bailey's Miss Hickory (the heroine is actually a doll, but interacts primarily with animals--slightly worrying at the end, but it all turns out all right, I always thought--and I read it a lot at that age);
-Thornton Burgess--I read several at her age and liked them well enough, but I find them really unbearable now--take a look and see what you think?
-Dick King-Smith wrote mostly animal stories (the Sheep-Pig, etc.)
-You already mentioned the Cat Club books--we have loved those here. Also The Voyage of QV66 (Penelope Lively)--but that one has not very many pictures.
I'll put my thinking toque on, and see what else I can come up with...
peace
minnie