Try the books listed cited by the Amelia Bloomer Project--here is the link:
http://libr.org/ftf/bloomer.html

Jessica even has a quote on the site :)

The Westing Game!

Reasons why I loved this book AND can keep loving it even now (massive spoilers ahead, since there's really no way to do this without them):

- Turtle Wexler is a 12-year-old girl. She is pretty much the opposite of the sparkly-princess ideal that society has now - she's outspoken, intelligent, and completely awesome. Through the course of the book she learns to kick butt at chess and the stock market. At the end of the book she takes over the Westing company.

Oh yes, and she's also the one who solves the book's overarching puzzle.

- You also have Angela Wexler, her sister, and the more conventionally beautiful one. Everyone in the book defines her by how pretty she is and how she's going to get married to a doctor. Angela resists this (although secretly at first). By the end of the book she breaks off the engagement and goes to med school herself!

For young kids (I think I was about 6 when I got this book) there's an awesome story by Norma Klein called "Girls Can be Anything." It's about a little girl and a little boy who are best friends. Whenever they play, he's the doctor she's the nurse, he's the pilot she serves drinks, etc. Her mom tells her girls can be anything, so by the end of the book they take turns being the pilot, doctor and president. It's a classic from 1975, but I think it's still relevant.

More praise - my post got interrupted.

I can't remember whether Angela goes back to Dr. Deere or not, but it wasn't emphasized.

Women of color aren't absent either. Judge Josie-Jo Ford is one of the more complex (and most intelligent) characters and gets plenty of 'screen time', but the book doesn't trivialize her past at all. Oh yes, and she ends up on the Supreme Court! Madame Hoo's story is treated well also - at the beginning of the story she doesn't have a voice (literally; she doesn't speak English) and has to put up with bigotry from her husband and other characters, but by the end she gets plenty of agency.

I could keep going but I think I've fangirled quite enough. Oh, and needless to say, the book passes the Bechdel Test about a million times over.

I loved the Joan Aiken Willoughby Chase series, which has a series of interesting girls in it. True, they are frequently helped by a boy, but they more than return the favour!

Trickster's Choice or Beka Cooper by Tamora Pierce; or really, any Pierce book.

These are more for teenagers than young girls...but they're still good...
The Earth, My Butt, and Other Big Round Things by Carolyn Mackler--Virginia, who's fat but from a family of thin people, starts off feeling very unsure of herself, thinks she's ugly, and idolizes her older brother, who doesn't care about her at all. But then when her brother rapes a girl at his college, she sees that he's not perfect after all and learns to stand up to her body-shaming mother. She also has a bit of a feminist awakening.

Hope Was Here by Joan Bauer--Hope moves with her strong, independent aunt, who's a cook, to a small town in Wisconsin, where she gets involved with a local movement to unseat the corrupt town mayor. There's romance in it, but it's not the focus of the book, and Hope and her boyfriend are clearly equals, and he never has to 'save' her or anything like that.

The Queen of Everything by Deb Caletti. Caletti has written several books for teenage girls, this one was her first and best, though. The main character, Jordan, is pretty stuck-up at the beginning of the book--she's popular, she's got a 'cool' boyfriend, and she has a job at a weight-loss center where she's paid to judge overweight people. But then some stuff starts happening with her dad (I don't want to give away anything), and she learns to be more authentic to herself instead of going along with the crowd, and to stop being so judgmental.

Harley, Like a Person by Cat Bauer. Harley learns to stand up to her parents (who are quite mean) and discovers some interesting family history in the process. I can't say much more except that it's good. Don't read the sequel, though, because it sucks.

Diva, by Alex Flinn. This is a sequel to Flinn's first book, Breathing Underwater, which focused on a boy who was abused by his father and in turn abused his girlfriend, but this story is told from the (now-ex)-girlfriend, Caitlin's, perspective. In it, she learns to heal from what happened to her, get over her ex-boyfriend, and get over her body issues and learn to love herself. She also repairs her fractured relationship with her mother. (Who also learns to stand up for herself in turn.) There's also lots of musical theater and opera references in it, as Caitlin wants to be an opera singer, which is interesting to a geek like me.