You can rent from the parks - but those will only be available to you IN each park and not to/from the buses or around the resort or anywhere else. And as a PP mentioned, they are hard plastic so some kids don't find them very comfortable.
Another option is to rent off-site for the length of your visit. This is likely less expensive than the park rentals, and usually a more comfortable stroller. I think many of the rental companies are using City Mini's as the regular strollers, or there are some "special needs" stroller for older/larger kids. However, these can be bulky for folding to ride buses.
A third option is to bring your own stroller - I'm not sure how comfortable a 9-year-old (even a small one) would be in a traditional baby stroller, especially if she hasn't been using it. When our DD outgrew the typical umbrella stroller we had used, we bought a Maclaren Major Elite. It's very similar to a typical umbrella stroller (folds easily/compactly, light-weight) just a little larger for older kids (up to 140lbs it said, but that might be a little over-generous). We ended up buying a used one for less than we would have rented it for the week. We rarely use it now, but we have it and toss it in the car for other vacation as "just in case."
If she's big enough, you might look into a pediatric wheelchair. But a small 9-year-old might prefer the stroller - depends on her view of such things.
As a note, she doesn't need to remain riding in the stroller the whole time. You can park it and walk for a bit if she'd like or need the exercise, then back to the stroller. Also, any CS restaurant in the parks will provide ice water for free just for asking - we bring refillable waterbottles and do this to stay hydrated.
Enjoy your vacation!