Have you been to Disney recently. I only ask because my then 2.5yo didn't want anything to do with a stroller. It didn't slow us down at all and were able to walk the way around Epcot and World Showcase. We didn't carry her at all. All kids are different but maybe don't rent one until you really need one. Maybe you won't need one at all.
Wow...I have a 2.5 year old now and 2 older ones and the 2.5 year olds not able to keep at the same pace as the rest of us on a normal day around home, let alone at Epcot. I just can't imagine any 2.5 year old walking the whole way around World Showcase, let alone at a regular adults speed. I think your kiddo would def. be the exception in those circumstances, so OP I'd just advise that it's probably not the norm and I'm guessing Epcot would be the park that they'd need a stroller the most.