Girly stuff that not too pink-princessy (if that makes sense): Little House on the Prairie, Little Women, The Penderwicks (my favorite storybook family!).
The Westing Game is a good one, but maybe a for older kids? Although if she's read Harry Potter she could probably read anything I'd be recommending.
Winnie the Pooh is actually not that easy to read, but very cute - it might give her a challenge.
Snow Treasure, by Marie McSwigan.
I second the Narnia series.
E. L. Konigsburg writes some really good stuff. Definitely unconventional, but I really love it.
I love Peter Pan, as well as the authorized sequel which is Peter Pan in Scarlet. None of that Disney junk.
When You Reach Me, by Rebecca Stead. Another one that may be a bit advanced but it sooo good.
What about Lloyd Alexander? He has lots of good adventures that aren't violent or scary - comfortable sort of adventures.
Avi also has lots of good books - Midnight Magic is a cool mystery.
Kate DiCamillo is awesome.
If she's into "boy" books, and she's read Harry Potter, then I would recommend the Ranger's Apprentice series by John Flanagan. They are violent, but I wouldn't say any more violent than HP.
A lot of my recommendations I would probably say are 4th grade reading level as well as maturity, if that makes sense, but if she's read Harry Potter I'd say that they're around that level or easier/for a younger audience.