DLR is much more compact than WDW (especially if you are staying at a nearby hotel), but DLR still requires quite a bit of walking. That said, we stopped using strollers once the kiddos passed the four-year mark. Our family tried to start taking evening strolls a couple of months before the trip. (Some weeks were better than others in regards to our consistency, though!). We also stayed on-site when our daughters were that age, and made a point of taking mid-day naps, having pool time and taking dinner breaks in DTD before heading back in to the parks.
Are you staying close enough to take breaks during the day? If not, I'd highly recommend mixing in more sit-down activities throughout the day (i.e., a circuit around on the railroad, Monorail, Tiki Room, Aladdin, Animation Studio, etc.). I also made sure the kids had two comfortable (and broken in!) pairs of walking shoes and tried to alternate the footwear each day. The stroller was convenient for storing items (though we had a jacket and a hat stollen out of them,so be careful!), but overall I'm so glad we don't have to deal with maneuvering a stroller through crowds or deal with parking one anymore.
Bottom line, though, always do what's best for you and your family. You know your child and your child's stamina best.