Strollers are available for rent throughout the Walt Disney World theme parks and Disney Springs.
The strollers at Disney World are hard plastic (easily cleaned) with a small canopy roof.  You can rent either a single, or a double wide, and discounts are available for multi-day length-of-stay rentals.
Important:  Disney strollers cannot be removed from the theme parks.  Therefore you won’t have a stroller available back at your resort or elsewhere on property.
However, there are many third-party companies in the Orlando area that will rent a single or double-wide “jogging” style stroller with delivery direct to your hotel room, that you can use everywhere on your trip – often for less money than renting from Disney.
Remember: many strollers look alike!  Distinguish yours from the rest by tying a fancy ribbon, bandana, or even Disney balloon to the handlebars so you can find your stroller in a crowd!