In most states, 3500 is that magic point where they require trailer brakes; for a good reason. I agree with the others that a trailer with two 3500 pound axles about 18' long would fit the bill perfectly for you. Those trailers won't cost much more than one like you mentioned. Be warned, everybody you know will want to borrow it though!

Two of my relatives ran into the back of other vehicles when they borrowed my trailer like that and
didn't have trailer brakes set up on their tow vehicle. Also, it is important to figure your actual amount you can haul as Bob pointed out.
I now don't worry about friends and neighbors borrowing my trailer. After a scary incident with my trailer loaded at it's max a couple of years ago, I bought a 30' gooseneck trailer with two 20k axles under it. The mfg tag on it rates it's net weight over 6000 pounds. Besides being a gooseneck trailer, the weight of the trailer alone exceeds most of their pickup's towing abilities; even if they have working trailer brakes.

You obviously don't need that, but if you have an FEL (or ever plan to get one) anything under 18' will be too short. I just about wore out the tail wheel on my bush hog once when hauling my tractor on the old 18' trailer. With an FEL and a 7' bush hog, I was still about 3' over the end of the trailer. Everytime there was a dip in the highway the tail wheel on the bush hog hit the road. I ended up having to replace it due to all the flat spots all over it.