Maxie,
Based on your location, I'm pretty sure you won't be driving to WDW! You will want to have your stroller in the airport, too. We always just bought an inexpensive umbrella stroller, carried it on the plane (or gate-checked it) and could always use it to carry the little-one thru the airport (or, pile the luggage on and have an impromptu luggage cart). It is certainly less expensive than renting for the whole visit, and as Cora said, you can wheel it right onto the monorail or boat if those are your modes of transportation. Also, you're out way less if, against the odds, it is misappropriated. When you get back home, put it away for the next visit!