I went through this a few years ago with my daughter when she was about the same age. At that time, the pediatrician acknowledged that my daughter was overweight for her height at 89 pounds (so it wasn't just me projecting my weight problems on her) but was adamantly against putting such a young child on a formal diet. Her recommendation was more along the lines of attempting to hold her weight where it was while her height caught up instead of trying to actually drop her body weight. Her reasoning on this was that kids who are growing (in height) can have their growth slowed down or even stopped by losing weight and cutting calories enough to cause weight loss can also deprive growing kids of very much needed nutrition.
About 9 months later, my daughter started taking medication for ADD and lost nearly 20 pounds in 6 months; no appetite because of the medication and she was deliberately not eating because her classmates had started teasing her about being chubby. Needless to say, her pediatrician was having a fit and right now we are under strict medical orders to not allow her to lose any more weight. She needs to have a height and weight check every other time she comes in for a refill on her medication, so they watch it closely. She's currently 4' 5" and 71 pounds (large boned).
My opinion is that there's nothing wrong with cutting out the obvious starches and sugars in your daughter's diet and instead replacing them with lower glycemic fruits and vegetables. How could such a thing be unhealthy? My kids still get the occasional high carb treat, but it's not a daily or even weekly thing. Talk to her about what bodies need to be strong and healthy. Another thing is to encourage her to excercise. Ask her to go for walks with you. Get her involved in some organized sport. Go bike riding or rollerblading together. That way, you both get excercise and you have the bonus of spending extra time together and limit how much time she spends sitting in front of the TV or computer.