I think your daughter will be exposed to all sorts of influences, not just religious ones. There will always be someone who will tell her what to think.
That magazine will tell her that she is not skinny enough, so she may want to skip a meal.
That boy will tell her all sorts of sweet nothings just to get into her pants.
That advertisement will tell her to buy things that she does not need.
You can't shelter her from everything out there, even from the influences of her friends. I remember watching the move Thank you for smoking. It is basically about this guy who is a lobby for the tobacco industry and there are many questionable things for the tobacco industry and he has to do this in front of his son. This presents a dilemma for him because he wants to keep his job and at the same time, he wants to teach his son the best lessons in life. Instead of teaching his son right from wrong, he teaches him how to think.
I genuinely believe that this is the best approach for parents to take. Teach your children how to think instead of what to think. I have a friend who has three kids. The youngest one is 7 and she came home from sunday school and told the mom about how they learned about the trinity. The teacher explained it by saying that God the father, God the Son and God the Holy Spirit can be compared to how water can take on the form of ice, liquid and gas. My friend was honest and replied by saying that she does not know and has not quite understood it herself. This stunned her daughter for a little bit because she must have expected a confirmation. Instead, she got a genuine answer from the mother. I must say that I notice that her daughter tends to be very open minded and welcoming when it comes to people of different religious or ethnic backgrounds and I believe this has to do with the honesty and the example that has been set by her mom.
If you can set an awesome example for your daughter, then it does not matter what outer influences are around her, because she will always have a center to orient herself around.