I built my retirement home from scratch, floor plan and blue prints through final painting. 3000 sq ft ranch-style, 4 bedrooms, two full baths. So I can do all the necessary plumbing, electrical, flooring, roofing and carpentry. The only thing I sub-contracted out was HVAC, concrete work, septic tank, and brick laying. But I would not tackle your project.
As others have noted, a TT is a lot different than a stick-built house. To begin with, your single-axle trailer is not "heavy duty" enough for more than a very minimal TT. Plus that looks like maybe a 16' trailer. A 16' TT is a tiny little thing. Look at the floorplans for a 16' TT and see if you'll be satisfied with that tiny TT. Adding an axle and appropriate suspension may be enough, but I suspect the frame would still be too light in the britches. You'll probably wind up spending more than a new lightweight TT would cost, but still not have a very good TT.
Here is the floorplan of my new TT that is 19' 6" inside length. It's tough to design a shorter TT and still have the aminities of a modern TT.
I agree with others that restoring an old TT would be a lot more likely to result in a successful project.
But if you insist on doing it with that utility trailer as the basis, then first be sure you have enough chassis underneath
to handle the weight of your wet and loaded finished product. Then design your floorplan down to the nearest inch. Design the walls and roof with high-strength, light-weight materiels. I'd use aluminum framing. If you don't know how to weld aluminum, then that's your first project - learn how to do it right and buy (or rent?) a good MIG welder that will do the job. If you attempt to stick-build it with the traditional 2x4 wood framing, you're going to wind up with a very heavy trailer.
After the framing is done, then add all the rough-in wiring for both 12-volt and 120-volt electric outlets, cable TV, antenna TV, etc. Be sure you use the correct gauge wiring for all circuits. The AC circuit will require a lot heavier gauge wiring than the light circuits. Then add the rough-in plumbing for kitchen, bath, holding tanks, etc. And don't forget to add the plumbing for the propane appliances and furnace. Decide on exactly which RV reefer and water heater you'll install, so you can have the correct rough-in wiring and gas plumbing for them.
Unless you have experience in designing a TT, then you'll probably want to have one with a floorplan similar to your dream parked nearby so you can constantly check on what's in it and how it's put together - before you install the rough-in wiring and plumbing.
That' gets you started. If you plan to pursue that project, keep us informed as to your progress.