Square sections are doable...
...but you're going to want radiused edges if you're serious about it.
If you're willing to adopt
airplane building principles, ignore these and build freebeard's zeppelin. But if you're more of a weekend carpenter I'd go with a box frame and generous radii.
I've been poking around regarding a pickup bed camper and have been banking on some pop-up elements to give more standing and sleeping room without sacrificing aerodynamics too much (5 degree taper on top). Maybe you could cut the frontal area significantly by popping up the top of your trailer!
Tent type
Hardtop type
Now, maybe the hardtop ones would be more applicable to your uses, but they could allow a much larger interior volume and better aero without giving up much but weight. If you were really into it, maybe you could fiberglass the top that hinges up, thereby avoiding the issue of building compound curvature with sheet metal.