Hello Misty! Thanks so much for your question.
Strollers rentals at Walt Disney World are not available to book ahead of time - they are strictly on a first-come, first-serve basis. If you click the link I provided, you can find out more information regarding prices, length of stay rentals, and rental locations. ( Although they show umbrella-type strollers in the pictures, they are actually not like those at all - they are much more sturdy and made of plastic.)
Another option you may want to consider, and one which may be more economical is to rent a double-stroller from an off-site provider. I recommend magicstrollers.com, as they are a very reliable company and their prices are reasonable. They will deliver and pick up the stroller from the resort you are staying at. Check out their website to find out more information.
I hope this information helps you with your planning, and I would be happy to answer any other questions you may have. Thanks for visiting the Disney Parks Moms Panel. Have a magical day!
Kristen