When DD1 was 1-2 years old I used to pull her and gear around RenFests all day at in a RadioFlyer wagon with big, inflatable tires. The faires take place in unpaved areas but the wagon could go over just about any terrain.

The downside though was I spent the whole day in a strange twisted shape to pull the wagon by it's handle. By the end of the day my back was very sore from this continous twist. I think a better solution would be to rig up some sort of pulling harness (with quick releases!) that would allow you to pull the wagon like a draft horse would rather than one hand/arm alway behind you.

-Blast