Welcome to the Disney Parks Moms Panel Angela!
I have always preferred bringing my own stroller but I typically drive to Disney World. Single and double strollers are
available for rent in all of the Disney theme parks. You can also rent single strollers at Downtown Disney. I don't think the strollers available for rent in the parks are very good for children that may want to take naps during the day. The strollers are made of hard plastic & do not recline so napping would be difficult. They do have a canopy and have a little (not a lot) of storage space. You can see a picture of them on allears.net. Its an unofficial Disney website but they do a great job of posting pictures of strollers.
Another option is renting from a local vendor like Orlando Stroller Rentals. They offer a variety of strollers, will deliver to your resort and are typically very reliable.
I answered a question for another Guest with some
tips on strollers that you may also find helpful.
Please feel free to visit with all of your planning questions. We're hEAR for you!
Wishing you minnie magical memories :-) Allison