I think you could easily rig such a trailer. The Toyota is supposed to be good for towing 3500 lbs.
If your trailer had a shower stall, chemical toilet, water tank w/pump w/ house battery, an on demand
water heater, and LP gas tank.....you would have all you need. A 12volt DC lighting fixture and perhaps a roof vent/fan could round out the build.
For really low bucks, you could find a large plastic basin for the shower and form a square frame of electricians conduit pipe the same size as the basin to hang a shower curtain from you could have a shower stall. You'd have to mount the frame on cross bars across the side walls of the trailer. Then make one of those 2 gallon garden sprayer showers that uses a kitchen sink sprayer/w hose spliced to the 2 gallon garden sprayer. This could eliminate the big water storage tank, pump, battery, and on demand hot water heater. And it would be a quick build.
You would only need to figure out a drain system for the basin. I have a large one that was my old Tom Cat's liter box when he was around with me. "rip". That box was probably 30 X 30 X 8.
Thetford RV plastic toilets makes some inexpensive chemical toilets. Not difficult to care for and can be emptied in restroom toilets or campground chemical toilet dump stations. They are in two pieces, the seat & lid and the tank below.
Here is a 2 1/2 minute Youtube Video that shows all of this:
Thetford Chemical Toilet Eaplained