Agree...you will have no issues with that size trailer. One question is...do you intend to keep the trailer for other use once you move? If not, then either just rent a u-haul or buy a used trailer and resell it after the move. If you do want to keep it, depending on your budget and personal preferences a used one can save you lots of money. If a new one is inevitable then there are lots of choices...You can get an ALL-Aluminum, or SteelFrame/aluminum body, or even wood frame/aluminum body, etc. What you buy will depend on your budget, how/where you will store it, and what you're going to haul in it.
I've got a lot of experience towing cargo trailers, here are some thoughts...
-A 7x16 will have dual axle...this is good and recommended highly.
-Typically will also have electric brakes, but some may not...make sure your does.
-Ramp door vs Barn doors - I find the ramp door to be very useful and well worth the cost.
-V-Nose versus Flat Front...this seems to bear some controversy, however I would argue that you can't calculate the effective difference between the two as far as fuel mileage, outside of perfect towing conditions. The trailer salespeople will tell you otherwise so you spend more...I say get which one you like better based on your use case.
I JUST SAW your last post and see your thinking on this. I would SERIOUSLY consider shopping for a used one. You would then be much less likely to take a financial hit. I would not expect to take a small loss on a used one...most people would simply opt for a new one if it were within a few hundred bucks. This size trailer is very popular with motorcycle riders/racers....search some racing forums, etc to see what you can find. I'd bet its much easier than you think and has less financial risk.