Depends just what level she's at (I have the impression that some children first read "independently" at much higher levels of decoding competence than others!), but for really easy stuff I'd recommend the Oxford Reading Tree Songbird Phonics. They are written for decoding, but (mostly?) by Julia Donaldson of Gruffalo fame, and there are some that DS5 still goes back to sometimes. If your DD is a bit further on than that, one thing that sticks in my mind is the set of Quentin Blake books we have - Cockatoos, Mrs Armitage books etc. Engaging words and funny pictures. Or the original Thomas the Tank Engine stories - we have a large book of all of them and probably that's what DS taught himself to read from, actually! Or if you're looking for chapter books (that kind of independently) he enjoyed the Worst Witch stories early on, or Winnie the Pooh, or... oh, it really depends on her interests, I could go on but it would be kind of random...
