Interesting concept...would end up making a heavy trailer...need a lot of truck in front of it. A friend of mine and I almost put an old Pinzgauer ambulance body on a trailer frame one time...but abandoned the idea because of weight.
From my (limited) trailer knowledge, a good set up has twice the gross weight rating of the load actually on it. The ambulance box probably weights well over a ton...add that to a frame with tires, suspension, brakes, axles...looking at an easy 2 tons of drag weight.
Would actually be a pretty good idea to drag behind an old 416 Unimog or something...could take the weight into some pretty remote places, detach the "home" and run some pretty hard trails.
We had a 3 ton army trailer (1.5 ton off road rating) that would take all our camping gear, and we bring A LOT of gear. Iit might have actually held an ambulance box, but I would think going a little bigger would be on the safe side...probably a double axle.