Here's a pic of the bottom of an old (1960's) Apache pop up trailer that I am making into a canoe/kayak trailer. As you can see, the framework is minimal, just a light weight X to mount the springs and the tongue, which is screwed to a 3/4 plywood floor. Across the front and rear are thin angles, that are mostly there for to mount the leveling feet. The steel is less than 1/8 thick, it might not even be 3/32nds thick.
The sides of this trailer are thin aluminum, with large doors in each side, so they don't add much strength (definatly not as much as the side of a TD would).
The "floor" under the bed is 3/8 plywood, with a thin aluminum support wall running under it down the middle, front to rear. When we were still using it as a camper, it had a 3" foam mattress on it, and seemed plenty strong.
If the darn thing was wider (it's only 4' at the outside) I would think about using that frame under my TD, to keep the weight down.