We all changed our eating habits. My husband and I switched to low-carb (for other reasons in addition to weight loss). Our daughter didn't eat as low-carb as we did, nor did she need to, but she did cut back on carbs/sugar a lot compared to what her diet was before.
We also started eating a lot less - and in our daughter's case, a bit less - on a consistent and prolonged basis.
The main thing is going to be portion control. For us, cutting out sugar and cutting back on other carbs helped with that, because it left room for more healthy, more filling foods, which, in turn, helped control hunger, so no one wanted to eat as much.
You don't strictly need to change your diet to lose weight. It all comes down to calories. However, if you're eating a lot of empty calories, you're going to be hungry a lot sooner, because there's no nutritional value in the food you're consuming. So switching to healthier foods is just going to make things easier for you, rather than feeling miserable and hungry all the time.
Encouraging her to be active is great for her overall health, and it will help some with weight loss, but losing weight is 90% diet.
And actually, at this stage, your goal shouldn't be for her to really lose weight. It should be for her to maintain her current weight until her body grows into it. She's about to hit puberty and undergo some big physical changes and she needs proper nutrition to do that, so you don't want to calorie restrict your 9yr old unless she's severely obese - and then it's best to follow a doctor's recommendation.
When I say we cut back on carbs, I don't want people to get the idea that our daughter went on some super extreme diet. Here's an example of a typical day of eating for her (she's 15, 5'5" and 128lbs):
So as you can see, it's not extreme, just more mindful.
And, of course, she does have other treats, candy, cake, pies, etc. on occasion, but they're jut that - occasional. She might have them once every few weeks.