Hi Savannah,
Thanks so much for visiting the Disney Parks Moms Panel with your question!
Whether to rent a stroller at Walt Disney World really depends on your specific child. I also have a 9-year-old daughter, and we do not rent a stroller for her. We have not used a stroller for her at Walt Disney World since she was about 4 years old; however, she has always been a very active child. For the past few years, she has been able to easily keep up with my husband and I at Walt Disney World. You need to consider your daughter and how you think that she will do with a day filled with walking to make this decision.
I would caution you to check the weight limits on the strollers if you are going to rent one for your 9-year-old. The weight limit for a single
stroller rented at Walt Disney World is 50 pounds, and I know that my 9-year-old weighs more than that. The page that I linked also has links to Disney Featured Providers for stroller rental, so you could check with them if they have single strollers with a higher weight limit. If you do rent from somewhere outside of Walt Disney World, you can absolutely get the stroller in to Walt Disney World. We brought our own stroller from home for years to Walt Disney World with no problem.
I hope that these thoughts are helpful for you, Savannah! Have a great time planning your vacation, and please do not hesitate to ask if you have any further questions.