Hi there Angela! I'm Angelo one of the newest Moms (Dads)!
Walt Disney World has many different transportation opportunities like the Monorails, Steamboats, Trains, and rides galore that should be a ton of fun for your three year old! To get around inside of the parks though from ride to ride, strollers are the way to go. If you do not want to bring your own, each park has a stroller
rental area where you can rent a single or a double stroller for the day. When you leave a park you simply turn your stroller in. If you are going to another park, keep your receipt so you can rent another one at the new park free of charge.
My kids have been for many years and we have used both our own and Disney's strollers. They always say how roomy and comfortable Disney's strollers are too.
All of the rides offer a great change of pace from sitting in the stroller so hopefully he'll be ok. Another way to get him around the parks is my tried and true piggy back ride. Trust me, I've logged many a mile with a kid on my back or shoulders, strollers rock!
I hope you have a Magical stay at the Walt Disney World Resort and if you have more questions don't hesitate to ask!