You might visit the RV and Motorhome Hall of Fame and look at the construction of trailers from the 1930s and 1940s, or find plans in Popular Science, Popular Mechanics and Mechanics Illustrated from the 40s and 50s when homebuilding was popular. It is not necessary to use the construction techniques employed by the RV industry today, when you already have a platform as solid as a car hauler.
Interesting that GlenL plans are still around. They were an important source for homebuilding of boats and RVs 50-60 years ago. Some of the materials might be hard to find (like Masonite and Celotex) having been since replaced by other products (mostly foam core) in housing construction.