My recommendation would be to go to the 6:00 show. I have 3 kids, and we have been going to WDW since my oldest was 4. Before we took our first trip, I remember reading about all the horror stories of children melting down because they were too tired and Mom and Dad tried to pack one too many things into their trip. Of course, only you know your child and how much she can tolerate, so you'll have to decide if staying up later will affect her the next day, or even a few days later.
I don't know how you are traveling or how long your trip will be, but that can be tiring as well. Maybe you could eat a big lunch and a light supper at 5 (or even a big snack around 4 - 4:30) and then grab some refreshments at the show.
If you're like us, the next day you will be wanting to get to one of the parks bright and early, so getting your child to bed at a decent hour the first night is probably a good idea. However, if you plan to sleep in the next day, the 9:00 show could work for you.
My rule of thumb on our
Disney vacations has always been that if we stay up late one night, we have a slower day the next, just to recuperate a bit. For instance, if we stay for Illuminations one night after being at a park most of the day, we might sleep in and go to a water park, swim at the resort, shop at Downtown Disney, play putt-putt golf, etc. We also take a break every afternoon and swim and nap. Even though your child is 7, she might benefit from a nap at least one day.
I know I've gone too long, but I just hate to see families who have pushed their kids too hard. Disney is wonderful and you want to pack in as much as possible in the short time you're there, but it's also hot, there's a lot of walking involved and it can be a sensory overload at times. Only you know what your child can handle. Hope my ramblings can help you decide what is best for your family!