We have had great success with some of the fairytale picture books. They are still picture books, which appeals to my young kids, but the stories are usually not twaddly, and the text is a bit more advanced than some other picture books. They may be a bit of a stretch for a new reader, but because of the pictures they have more clues available to help figure out unfamiliar words.
One series I recommend for when your DD’s reading is a bit stronger is the “Fairy Realm” series by Emily Rodda. We started them as read alouds when my DD was five, and then she went back and reread them all independently. They are about a girl who finds out that her Grandma was a fairy princess and then travels to the Grandma’s home world (The Fairy Realm) for lots of adventures. They are light reading, but not nearly as twaddly as some of the other princess and fairy books around. Even I enjoyed the stories. There are ten books in the series. You could probably read the first couple together and then let her take over.
Here is some my DD has enjoyed (she’s six, but a strong early reader):
Mrs. Piggle Wiggle
Milly Molly Mandy
Rowan of Rin (another series by Emily Rodda)
Magic Treehouse (I’d call this semi-twaddle, but my kids really enjoy them and learn a bit about history, so we allow them)
Raggedy Ann and Andy
Boxcar Children
Secret Seven by Enid Blyton (she wrote many other series, but this is the one we’ve got)
She also LOVES a series called “The Puppy Place” and another called “Kitty Korner” Definitely twaddle, but she loves animals, so we compromised a bit. They are cute little stories about a family who foster animals and find good homes for them.
Joanne