Your daughter is perfectly healthy and beautiful. And I think it is normal for young girls to think they are overweight even though they may not be.
Since she seems pretty determined, (as in she'd want to lose weight anyways), maybe your help and approval may be beneficial in this situation. Eating healthy (more salads, less meat) and more exercise is the safe way to go as people have already mentioned. If you like to do any sports or outside activities together, do that, be it running, jogging, bicycling. Be active in her life and see what she wants to do, then see as a parent if that's a good idea.
The media plays a big role in shaping the way people and especially teenagers may think. They can often compare themselves with the super skinny, unhealthy celebrities they see in magazines or on TV, people who can set pretty bad examples for today's youth in terms of lifestyle.
You sound like a great role model for her, Lexi's Mommy, so keep it up! She sounds very well-rounded. Give her the support she needs and she'll continue to be the great daughter she is.