There are Disney Fairy books. There's The Trouble with Tink, A Masterpiece for Bess, Fira and the Full Moon (I think). There are a few others as well.
You would be surprised what a 3 year old can "get into". DD has loved the Disney Fairies and read all the ones at our libraries. What she loves even more is the Rainbow Magic Fairies by Daisy Meadows. We've asked the library to order in the most recent ones. She's read all of them (there's about 40 in the series). I realize that's not what you were asking for as they aren't traditional fairy tales, but if she liked the Disney princesses, she may like these as well. Besides, traditional fairy tales often have scary undertones.
FWIW, our DD isn't even into princesses and fairies. She prefers pirates, skeletons and all things to do with the human body, but she loves these fairy books. She has no interest in fairies whatsoever outside the stories.