At this stage of her adolescent development, your daughter is searching for a comfortable identity. She is going to try out different "looks" in an effort to be more accepted by her peers. She wants to fit in somewhere and she might believe that changing her hair color, wearing a certain style of clothes, or listening to a particular type of music might help her to fit in. She also might simply want to see if red hair looks "cool."
Parents shouldn't engage their teens in battles over hairstyles, hair color, or clothing. As long as your teen's fashion and identity statements/experiments don't present clear health problems, I would let her experiment. Attempting to change her mind by forbidding her to look a certain way or punishing her for doing so will backfire and create an unnecessary break in your relationship.