Mike, as to when trailer brakes become necessary, there are lots of opinions, but one old federal recommendation was to require trailer brakes any time the weight of the trailer exceeded 40% of the weight of the tow vehicle. Not a bad recommendation in my opinion.
You mention a 3500 pound axle (singular). Now I certainly don't know for sure, but when you talk about 3/4" plywood floor, building shelves (and of course they need to be built to keep the merchandise from falling off the shelves when underway), and an enclosed trailer which means walls, roof, and doors, plus the merchandise, the weight starts adding up pretty fast. Maybe a single axle is enough, but I wouldn't bet on it.
You may also want to consider a trailer with shock absorbers. I don't know how important they will be for your merchandise, but I learned long ago that I wouldn't want an RV without shocks.
Almost any RV supply place will have locks for the coupler when the trailer is not coupled to the car.