Beyond the very basic chapter book series like Magic School Bus, Magic Puppy/Kitty and alike, here are some ideas that your dd may like:
- Time warp trio series (short but fun and decent reading level)
- Moongobble series (easy reads but superfun)
- Little Wolf series (easy reads but superfun)
- Franny K. Stein series (easy reads but superfun)
- Who shrunk Daniel Funk series
- Cornelia Funke has a book about a dragon and one about a princess that are higher level reading and my dd loved them at 4ish
The other series my dd loves may not be Ok for a sensitive little girl (mine was fine with these and she loves, loves Roald Dahl): Percy Jackson, the 39 clues, the Red Pyramid, the How to Train Your Dragon Series
Hope you can find something that works here, if not let me know, I've been on this road with my 5 yo and should be able to dig up more ideas, though my dd is not sensitive.