If your daughter likes fantasy/adventure, these are a little gentler. You might still want to read them in advance but most of these still hold up for adults. This type of book always has a lot of conflict, but I think these are less frightening than some others. My DD9 is also very sensitive but she has been able to handle these.

The Name of This Book is Secret (Series) - Pseudonymous Bosch (Have to admit I haven't read it, but DD liked it.)

The Chronicles of Prydain (Series)- Lloyd Alexander (Maybe a little scary but also has humor)

The Dark is Rising (Series)- Susan Cooper

The Chronicles of Narnia- C.S Lewis (unless you think she would be upset when
Aslan dies even though he does come back to life)

Percy Jackson and the Olympians (Series)- Rick Riordan (Poster above mentioned this. I agree! These are really fun books.)

Other gentler books my kids have enjoyed. . .

The Borrowers- Mary Norton

Pippi Longstocking- Astrid Lindgren

Mrs. Piggle-Wiggle- Betty MacDonald (Easy reading, but it's funny and nothing traumatic happens)

Caddie Woodlawn- Carol Ryrie Brink

From the Mixed Up Files of Mrs Basil E. Frankweiler- E.L. Konigsburg

I would definitely avoid all the classic books in which animals die. Where the Red Fern Grows, Sounder, Old Yeller, The Yearling, etc. If your DD is sensitive, these would be devastating to read right not. Great stories for another time, though.

This post is getting too long. That's what happens when you ask a book lover . . .

Good luck!