On your way past an RV dealer, stop in. You would be surprised at how little there is there.
The walls are a light sheetmetal. If you can find some inexpensive aluminum siding (know anybody replacing it on their house with vinyl?) Vinyl siding is pretty strong too. You treat the leading edges well, and it should hold on going down the road at 60.
Old offset printing plates work well, you scribe an X corner to corner to make it more rigid. We did this with an earlier fishhouse. It's hard to find printing presses that aren't all digital now though - we found some local newspaper plates 20 years ago maybe. You could read the paper through the paint. It was pretty cool
You could also fiberglass the outside - think fiberglassed wood hull kayak/canoe/boat. Light, strong, and durable. It's also very paintable.
I would build it out of 2x2s, 2x4s ripped in half. This is strong enough if you brace it well.
If you where ask me to design one today, it would be 2x2 construction, half inch plyood floor, 3/8s inch plywood roof. Walls would be foam sheet filled. Either tarp or that plastic paneling board used in bathrooms, commercial kitchens, etc. The inside would be wood paneling. The roof would be a rubber roof over the plywood. I can see putting some aluminum or metal angle on the outside corners to help with tree branch strikes.
Hrmm, maybe find an old trailer house, scrap that out for stuff? Sheet metal, windows, etc. Metal prices are pretty low right now though. Won't work if your in the city or if the Missus likes a nice yard.
Ah, I think your best bet is to watch craigslist or freecycle and look for a pickup camper. You can dissemble it, and reassemble it into your trailer. Most all the parts you need, stove, sink, furnace, door, windows, sheet metal, etc.