When we were there last year, our kids were 3 and 5. The oldest did not normally use the stroller otherwise, but we were really glad we had strollers at WDW. We actually took our 'regular' stroller and an unmrella stroller 'just in case' for the 5 yr old. Well, Just in Case became ALL the Time and we were all glad. For one thing, it keeps little ones with mom and dad without constantly hand holding and running to keep up. WDW is a big place with crowds and my kids felt safer in their strollers while we were moving from place to place. YES, you need one. If the child is upset by the idea, tell him it is to carry your day bag, camera, etc (which is really handy too.) However, once there, he will want to ride before long.
In my opinion, whether to take your own depends on where you are staying. We never felt the stroller a burden IN the parks, but on the bus, they were a BIG issue. Monorail wasn't quite so bad. If you are staying somewhere that uses busses a lot,
rent a stroller at the park. If you park hop or leave the park and come back, keep your receipt and get another when you return.
While you are in the park on rides, etc, you just leave it at the entrance to the line. There is 'stroller parking' everywhere. Sometimes the CMs will move them a little while you are on the ride, but this is not a big deal.
Good luck