I've done it twice, both times with a stroller in tow. It's Disney, so everywhere you go is handicapped accessible so the stroller is no problem. When you book they'll tell you they welcome strollers.
The only thing I would warn you about is when they go into a ride you'll have to park and grab your child and rush a bit to catch up. The tour guides are very accommodating, as someone else mentioned, so you shouldn't panic. The only reason I bring this up is so that you don't have too many valuables in your stroller and get caught by surprise when having to dump it.
Also, without giving anything away, I think I can tell you that at one point you may have to head into Cosmic Ray's via the stairs. Both times I just went around to the door with the ramp and met the tour inside. It actually put me in a better place to take pictures as the kiddos came into the restaurant.
It's a lot of walking, etc., so to try to do it without the stroller, IMHO, would be a nightmare.
Have fun!