Have you seen BikesAtWork.com? They sell bike trailers that would make an excellent base for your design. Even if you don't want to buy an entire trailer, they sell their hitches separately, which could solve your problem of how to connect the bike to the trailer.
Another option you might think about would be to use a metal framework or mesh, covered with Tyvek or some other lightweight tarp-like material. I suggest a mesh because it could keep the walls stiffer and less likely to billow in the wind. It would be quite a bit lighter than half inch plywood.