Well the great thing about the library is that you can borrow these books now and if she's not interested in reading them yet, return them and try again at a later date :-). The "appropriateness" will vary from kid to kid at this age IMO - there are some who will be totally enthralled by the books (speaking of the picture ones, there are also MSB 'chapter books') and others who would be indifferent or not ready to sit still for them yet. My daughters enjoyed the books when they were around kindy/1st grade.
I'm copying a reply I made to another post about chapter books to read to preschoolers - in addition to the ones listed below, Ron Roy's "A to Z Mysteries" series is great for early elementary kids, as are David Adler's Cam Jansen mysteries (there's also some "Young Cam Jansen" books that are shorter, good for reading with kindergarteners or for young readers to read themselves). There's also the "Nancy Drew Notebooks" which feature an elementary-school-aged Nancy who tackles age-appropriate mysteries like the stolen birthday party invitations.
I'd browse the "early readers" section of your library and pick a few to see if they hold your kids' interest - IMO Nancy Drew might be a bit boring to a lot of preschoolers and Narnia a bit intense, but my kids are a bit on the sensitive side so that might just be my experience. And I don't think my kids were really ready to sit for books like Little House until around 1st grade, but we *did* find our library had "My First Little House" books that took excerpts from the original stories and expanded the illustrations in picture book format, which was a good introduction to the stories. Scholastic also publishes "Little House Chapter Books" which take excerpts from the original books, simplify the language a bit, and group them by theme (for example, the "School Days" book uses a few chapters about Laura and Carrie going to new schools from On the Banks of Plum Creek and the Long Winter)
Some that might be worth checking out:
Kate Di Camillo's "Mercy Watson" books - crazy silly adventures of a family with a spoiled pet pig, accompanied by crazy silly illustrations.
Syd Hoff's "Danny and the Dinosaur" stories
Rosemary Wells' "Yoko and Friends School Days" books (These were among the first chapter books I read to my daughters when they were around 3-4YO)
Mo Willems' "Elephant and Piggy" books
Dav Pilkey's "Dragon" stories