My mother told me that when I was younger, I would refuse to eat much, much like what must be going on with your daughter. My mother let me eat whatever I wanted, since I was so skinny and she thought I'd starve to death, but in retrospect, it created really poor eating habits that were hard to break. A sugar addiction, among other things.

So my advice is to keep her diet as balanced as possible when she eats. Aside from that, you don't need to worry. Kids won't starve themselves.