If all you plan to move in the trailer is the robot, pit, and promotional items, you should be able to do this in well under 3500 pounds gross trailer weight. We went with a much larger (16'x7') trailer because we are using it as on-site storage as well as mobility.
If you're going to invest in the money for a trailer, seriously consider going the extra mile and making it loud. We found a local guy to
wrap our trailer based on a student-generated rough design and his artwork for a few hundred dollars (he did the work at cost). (OBTW, the tiger tearing slits in the image is a recurring Slidell High element/meme; see
our 2016 gonfalon, e.g. my current avatar, for another example.) As the trailer is stored on school grounds, it is a regular billboard helping promote awareness of the team.
For power, we went a somewhat different route. We installed solar panels on the roof, and a combination 12V battery charger/110VAC inverter system from a local dealer in solar systems.
Consider how you will secure items in the trailer. There are a number of pre-fab systems, or you could just put in padeyes and use cargo straps or lines, but the easier it is to use, the more likely it is to be used, and the less likely that you'll lose a load.
That video above about proper loading is absolutely true. About a dozen years ago, I loaded an 8' long sofa into a trailer made from a 6' long pickup bed. Moving off of the interstate onto the low roads wasn't enough, even without random sideways forces - I eventually realized that I had a negative tongue weight, and the ball was coming unscrewed from the nut. After re-securing the ball, I had to relocate the sofa to a rather unusual situation (tailgate closed, sofa propped up at a weird angle and strapped down rather than forward), but it got me home safely. The tongue weight of a trailer should normally be 10% of its gross weight - pushing DOWN.
As a way to get a handle on your tongue weight without special equipment, watch how far down the towing vehicle moves when a person who weighs about 175# stands on the ball. A trailer with a gross weight of 3500# should push the back of the towing vehicle down about twice that far. If it doesn't move down far enough, re-balance the load!