I agree, a cart with two large bicycle tires and maybe two hand holds you can stand between to pull it would be better for rough terrain. Something like a scaled down rickshaw.

We have a cart like the one shown that we use for carrying horse feed and trash cans. It's effective, but not something I'd want to pull for very far. One problem is it puts you into an uncomfortable posture to haul it. Another is that four tires like that provide two much resistance over even mildly rough terrain.