For rabbits, I would definitely roof the whole thing. Rabbits do better with plenty of shade, and when they do not get wet from rain.Gorrila cart tires in the front. Legs in the back. Use wheelbarror arms for moving it, slot them in. Maybe 4' x 4' cage. Probably build a box in one corner for the wind and rain, so I don't have to roof the whole thing. Maybe green polycarbonate?
I'm not sure which kind of polycarbonate you have in mind-- opaque might be fine, but I do not think transparent would be a good choice for a roof over rabbits.
Other than the roof, your idea sounds to me like it might work well.