I would just like to add that I remember being that age and I was always hungry! I was also a very active kid, though, always riding bikes, playing outside, going on walks with my mom, etc. I was also in dance and when I was 11 or 12 I started mowing my neighbor's lawn and walking her dog. I was always stick-thin and had no problems eating as much as I did at the time because I was active. But my point is that it's completely normal to be extra-hungry at that age! Girls are growing like crazy from about 9-13 and actually do NEED those extra calories. You as the parent just have to make sure the calories she's getting are healthy ones. Limit soda and juices b/c they are full of sugar. Limit desserts and junk food like chips. Have healthy snacks like fresh fruit and veges with dip, granola bars, popcorn, tortilla chips with salsa, etc. And let her have seconds or thirds at dinner if she's hungry! It's actually worse to not let her eat if she's hungry b/c her body will recognize that it's not getting the calories it needs, so it will start storing fat to use later in case she starts eating less or doesn't have food. It's nature's way of preventing the body from starving. So let her eat as long as she's really hungry! Try having her drink a full glass of water after each plate of food, though, b/c sometimes our brain mixes up the signals for hunger and thirst.
And you really need to get her active in something as soon as possible. Most cities offer inexpensive sports and sometimes dance programs. Have her try each one for at least 2 or 3 months before she decides if she likes it or not. Keep trying until you find something she really enjoys! Soccer, basketball, softball, swimming, dance, gymnastics, cheer, tumbling, or even archery or rock climbing. You could even look around at gyms and see if there's one that offers kids' fitness classes. You should also look into getting a Wii or Xbox 360 Kinect. Both great ways for kids to stay active, but think they're just having fun playing video games LOL You could also try biking, walking, or hiking as a family. See if there's a park in your area with a nice walking trail. If there's a lake near where you live, try kayaking.
The point is not that she needs to lose weight, but that she needs to be healthy. She needs to start learning what foods are good for her body and which ones aren't, and that it's ok to have junk food in moderation. She needs to learn that staying active should be a way of life, and that exercise can be fun.