Well, I'm kind of torn on this one. I totally get wanting to have a stroller - our first visit was when my little guy (now middle guy!) was 3.5. He still needed a stroller at times and it was just plain handy to have.
First, how big is your kiddo? Buying a cheap stroller there might mean discomfort for your little one, as many of the small cheapies are, well, small.

Also, do you need a basket to lug stuff around, like water bottles, souvenirs, snacks, etc? Again, might have trouble getting a basket with a $15 throwaway umbrella stroller.
I've traveled by plane tons with my 3 kiddos and we've checked countless strollers. So far, we've had pretty good luck. I like to bring my Chicco Liteway and just tuck it into a bag (you can find these on Amazon.com or many baby gear websites) before gate-checking it. Of course, if you have a larger, more cumbersome stroller, this isn't going to be an option for you.
I've never done it, but I've heard really good things about the stroller rental places that cater to WDW visitors - perhaps this is an option? Or you might consider renting a stroller from WDW. I think these might provide one that's large enough to accommodate an older kiddo while still giving you a bit of storage room AND giving you peace of mind that your personal stroller isn't going to be chewed up by airplane travel.
