I have a child that age, and I teach children a bit older. I will tell you--it doesn't have to cost much to entertain them. Often, they just like to free-play or have your attention.
If she enjoys swimming and the day is nice enough, that will likely fill much of the day right there. My kids love swimming, and I get bored with it much sooner than they do.
If she enjoys art, the Art of Animation has free art classes where they teach them to draw some of their cartoons. We stayed at AoA on our last trip, and just walking the grounds was fun for our kids.
Many people enjoy visiting the Animal Kingdom Lodge to look at the animals, and that is free. Many have mentioned the camp fire sing-along at Fort Wilderness Campground. The campfire and sing-along are free, but you would either need to bring your own s'mores ingredients and sticks, or you would need to buy a s'mores kit when you get there. I can't remember the price, but I don't think it is much.
I would be afraid that Disney Springs might open up your wallet if you aren't careful. lol I would reserve DS in case it rains and you need to take her bowling or to a movie. Bibbidi Bobbidi Boutique might not be much more than that. I think I paid $60ish + tip last time we went. We did not buy a princess dress there, however. If it is something that you would spring for, I would ask her dad to send her with a princess dress, and she can change into it there. (They are very used to people bringing in their own dresses, and they have special dressing rooms at the Disney Springs location with the Fairy Godmother that talks to her in the mirror.)
Some children (and teens and adults) enjoy riding the monorail. If she likes boats, you can also take a monorail from the Poly to the Contemporary, then hop a boat and ride it around. It picks up/drops off people at the Contemporary, Fort Wilderness Campground, Wilderness Lodge, and the Magic Kingdom.
Many have mentioned the beach (just stay away from the water) and the fireworks. And a Dole whip from the Poly. The outdoor movies at the pool.
Fort Wilderness Campground hosts a hayride. I think it is somewhere in the neighborhood of $8 per person. Not positive on that.
If you don't mind bringing an Uno or SkipBo game, kids that age often enjoy playing games like that. She might enjoy sitting in the Poly lobby playing games.