I can see that you already said you're not going to rent one there and that's good. I just want to say that I can't believe so many people are recommending the Disney strollers.
I've been to Disney a million times but this January was the first time we've ever went with kids. We had a 7 month old and a 17 month old with us and rented a double stroller at the Magic Kingdom (I'm not sure of the price because my cousin works for Disney and got us one for free).
The Disney stroller was horrible! It does not recline, so there was no way for a kid to take a nap in it. It was all plastic including the seat so there wasn't even any padding in it. The safety strap was only a waist belt and didn't even go between the legs! My 7 month old nephew couldn't stay sitting up in it (he kept flopping over to one side) and my poor sister and bil had to carry him around the park. I kept my 17mo in an Ergo baby carrier (this was the BEST option, worked great!). We got stuck pushing that stroller all around the park...but at least we used it to hold our diaper bags.
It is big, though, so for children who are maybe 2yo or older that can hold themselves in well and get tired walking...this will work...but they won't be able to nap in it.