I hope this isn't too rambling, but eating is a really big issue wiht me and how I parent, so a lot came ot mind.
I am torn about what the pediatrician said. On one hand if s/he isn't worried, then I would hate for you to creat a weight issue wiht her. She may not be thin, but is she genuinely overweight? At anyweight, I would never tell her she needs to DIET - I would teach her to shop and eat appropriately and nutritionsly. And if the whole family needs to change then so be it. YOu can be thin and very unhealthy.
On the other hand, the pediatrician should be looking at BMI, not just weight. Do you know her BMI. USe tha tas your guide. Also, the pediatirican should be asking you about diet and exercise, not just weight and BMI. Some kids can be really thin and terribly unhealthy. Maybe a different pediatirican could help you focus on the issues better.
The best gift you can give to your daughter is to teach her how to shop and cook healthy meals. Teach her to grocery shop by avoiding the center of the store and eat whole foods (such as pieces of fruit, not juice), drink only water, and don't eat anything from a package (chips, cookies, mac n'sheese).
Teach her to be creative. If she wants a sweet, dip fruit in dark chocolate or bake from scratch. If she wants chips, cut up and bake tortilla chips. Make smoothies with fruit and yogurt instead of ice cream.
Think about a cooking class with her that focuses on nutrition. Ask for a referral to a nutritionist.
It is great you have her moving. Make sure she is active at home too, with chores and going for walks as a family. Not just sports and classes. Focus on LIFESTYLE and not just losing weight. Basically, whatever her level of physical activity, she is taking in more caleries than she is burning. You and your family need to make a dietary adjustment to the types of food and maybe the portions. Make sure you are honest with yourself about what food you have in the hosue. Why would she eat any "junk food"?? The only time my kids get sweets or "junk" is when they go to a party or event like a festival. We are a juice free home and bring in desserts only when we entertain. I don't say "no" a lot, I just don't have junk in the house so it is a non-isse. Even when we do treat ourselves, we drink only water and keep portions small.
Teach her to focus on feeling full and not overeating. Teach her tricks like dringing water before a meal to fill up and prevent dehydration. Eat saladas and veggies first, before the entree. Eat low fat dairy. Eat plant-based foods like eating bean burritos instead of beef or chiken.
Also, a great book is "Healthiest Kid in the Neighborhood" (Dr. Sears). It is a great resource for adults, not just kids.