I am looking to fill my daughter's shelves with some books that are empowering for young girls.  Books that will show her she is a strong, beautiful person who does not need anyone to come rescue her and that she is perfect the way she is. I have a few already like the Paper Bag Princess. Any other suggestions?

It is not clear whether you want picture books or chapter books.  There are lots of books for kids these days with a strong young female protagonist.  Igraine the Brave by Cornelia Funke comes to mind.  My daughter also really likes the Sisters Grimm series, though I haven't read them. 

A few oldies but goodies:  Island of the Blue Dolphins by Scott O'Dell and Jacob Have I Loved by Katherine Patterson (the title is a biblical quote - there is no Jacob character or love story). 

For a young adult, the first book of the Hunger Games features a strong and independent woman (and there is a bit of a reversal from "traditional" gender roles in that one, as the female is an independent hunter and the male lead is more sensitive, artistic, and dependent on her for survival).  However, due to its violent content it really isn't appropriate for anyone younger than at least 14-15, IMHO.

I checked in with my little experts.  For picture books, we'd recommend The Princess Knight (again by Cornelia Funke) and Eleanor, Ellatony, Ellencakes, and Me (not an adventure, but a self-determined little girl - and in verse to boot).  For beginning readers, the Junie B. Jones books.

I second the Sisters Grimm recommendation.

Most anything by Jane Yolen - she has picture books and chapter books. Ballad of the Pirate Queens, Sword of the Rightful King (fun girl power twist on Arthurian legends), Not One Damsel in Distress (folk tales), and she has a bunch of retellings of fairy tales with strong heroines.

Enchanted Forest Chronicles by Patricia C Wrede.