While you should definitely vet the content of movies you let your child watch, Disney movies are perhaps the least problematic in this regard.
Let's look at a few Disney movies with these Princess characters. I'm going to limit it to the previous century to avoid an incredibly unweildy list problem.
Here right off the bat we do have a problem. Snow White is at its very core a story about beauty, and a princess who is envied for her beauty, and who wishes for her prince to come one day to rescue her. So it could be problematic, but let's look at it a little closer.
While it's true that Snow White's most lauded attribute is her beauty, it's clear that she has many other positive features - humbleness and kindness.
Let's also consider that while she is the focus of the story, she's not the lead actor of the peice - the dwarves by far do much more than she does, and will likely be what entertains your child most.
Still, you may want to wait this one out until your child is better-acquainted with princesses, given Snow White's lack of direct involvement in her own destiny.
This one might be problematic too. The premise is of a daughter who has natural beauty that the wicked stepmother and her stepsisters are jealous of, and that only by getting a special chance to go to the ball and impress the prince with her beauty can she escape this lifestyle. While she does show some personal talents and resolve, this is probably the movie where most of the princess-complex fear comes from.
Still, it's not nearly as bad as you might think. Her 'beauty' comes more from the way she conducts herself - far more humble and kindhearted than her wicked sisters.
Alice In Wonderland
She counts, she definitely counts, and is definitely a major departure from the previous two characters. Not only is there not even a hint of her acting like a typical princess, she's an independent, self-driven character. The whole story is very...abstract in any case, so you really don't have to worry about any princess complex developing from this at all.
I'm mentioning this one because of Wendy. She plays a very prominent role in the story, and could even be considered a protagonist in her own right.
Lady and the Tramp
Do dogs count? Bit of a wash here, more about preconceptions of beauty than anything else.
You might be surprised that this movie paints a rather progressive picture of Aurora (the princess) who certainly has dreams of meeting a handsome prince, but is also a lively, progressive and imaginative character, and not just motivation for the prince's crusade (In fact, at the beginning the young prince who's arranged to marry the newborn baby is amusingly disgusted by the idea, just like a young boy would be). You might run into some trouble with the fairy 'gifts' to her though.
Do CATS count? Maybe...the female leads aren't exactly pro-active, but the young child and mother cat are just that, and really aren't anything to be concerned over.
Do Foxes-Okay let's just say they count. Maid Merrian instantly falls in love with Robin Hood and is the object of his affection, and doesn't do quite enough to warrant herself as a progressive heroine type, and there isn't much to make up for it either. It's a very simple movie.
The Little Mermaid
Aaaah, okay then, here's a movie that is RIFE with problematic messages. A young princess whose beauty and gorgeous voice is renouned who gives up her entire life to be with some guy she just saw on the beach one day. Giving up her VOICE no less. And endangering her whole family. Granted, she has very independent tastes of her own and a fascination to know more than what she's been given in life, but I can definitely see a lot of red flags going up in terms of 'will this send the wrong message to my child'.
Beauty and the Beast
Okay, this movie has two sides to it that need to be addressed.
On one hand, you have Belle in the countryside, who is book-focused and intellectual against the provincial lifestyle of the townsfolk, right up to outright rejecting the boorish nature of the town's favorite man Gaston (who no one is like in any way). There's a lot to be said about the positive message sent here...
And then she gets captured by a Beast...she still loves reading, and she still has an independent nature, but there's something very...captured-princess about her siutation that might rub you the wrong way.
Still, if you don't mind the message that you can find beauty under something that looks ugly, it's definitely not a bad choice.
Jasmine's attire immediately brings up some concerns here. But let's try to look past that. She's definitely treated at the start of a movie as an object to be won, which she is vehemently against, to the point of running away and objecting to every sutor sent to her. It definitely teaches that there's much more to a girl than just 'being the beauty to be won', though it may emphasize an idealistic 'true love' a bit more than you'd care for. If not though, Jasmine's not a bad role model.
The Lion King
I'm going to say lions don't count.
It's been awhile since I really saw this movie, but Pocahontas has a LOT more going for her than just pure beauty. She's free-spirited, wise in her own way, and very strong, even stopping a war. Not a bad choice, though you might want to vet this one more personally for other reasons.
The Hunchback of Notre Dame
Esmerelda's fairly independent. I don't remember this movie all that well, but she doesn't give of a huge princess vibe from what I can remember...
Could be problematic. Meg's chief characteristic is that she's a princess that Herclues 'saves' and that she falls in love with him, something that gets used against him in the end, and that he gives up Godhood for.
...Okay I could go on forever about this one, but if you need any evidence that there are movies with Disney 'princesses' who do more than just sit around and wait for a prince to rescue them, just take this movie and watch it with your daughter.
I'll call this one a wash, since the leading lady is an anthropologist who winds up staying in the jungle with Tarzan.
All in All
If you're really concerned about your daughter latching on to the idea of being a princess, there may be one or two movies that would re-enforce that, but not nearly to the degree you might think.
You should also note that regardless of what movies you expose your daughter to, she IS going to be exposed to this, one way or another, without your own input. It's ingrained into our culture. Her friends or family friends or even just TV commercials will introduce her to the idea, and it's better that you expose it to her in as positive a way as you can then to just let her find out about it on her own.
What you might want to at least try to avoid, however, is the Disney Princess toy line. Toys that wash away these positive self-asserting aspects of the character and make them into little more than just princesses wearing cute dresses and tittering about castles all day.
...Or if you feel like your daughter can handle it, just get a few toys for her and introduce her to a few positive female role models on your own. A single movie or a few needlessly pandering toys aren't going to ruin your child's self-image. Not if you're there to answer her questions about what being a princess really means.