I haven't read any of the responses, but here's my two cents:
We are big Disney fans. I had seen the various movies with princesses before any of my kids were born, and Mulan has always been my favorite. I am 1/2 Iranian, and my oldest daughter is dark like me. Rather than gravitate to a princess who looked more like her and shared some of her cultural background, like Jasmine, my daughter fell in love with Cinderella and Sleeping Beauty. I let her like the princesses. As she got old enough to understand, we talked about the movies and the role of the girls in them. She has always known that I love Mulan and why. My daughter is almost nine now. She is very into fancy, girly things. She also has way better self-esteem than I ever did. She's smart and into science in a big way. She adores science-fiction and other non-girly-girl things. I think we're doing a great job of raising her to be confident and to love herself
This is happening even though she adored princesses...My three year old has recently discovered them, and that's fine with me.
If your daughter loves Cinderella, I highly recommend the newer movie Cinderella 3. In it, the evil stepmother reverses time. Cinderella must find a way to win her prince on her own. I think it will calm some of your fears about an overly dependant character.