Sounds like a great find. Welcome to airstreaming.
Your truck will do very well. Hitch height might be an issue. I seem to remember that mine is around 19" from the ground. You only need to be close for one short trip. Ideally, you should get the trailer level so that all tires carry the same amount of weight. And you don't want the tail dragging. Usually the hitch ball can be adjusted approximately 4" or 4 notches, bolt holes, etc. The hitch ball will be 2&5/16", 10,000# rated. I think you use about 10-15 degrees downward tilt on the ball.
My 1987 Sovereign
29' has a hitch weight of 810lbs & actual weight of 6600 lbs so your 31' should be close to the same. I think your axles are rated the same as mine at 6800lbs gvwr.
Tires should be load range D or 2540lbs per tire inflated to 65psi. The wheels are 15" dia and are probably rated for 2600+ lbs per.
I alway use a jack point between the tires to access a heavy part of the frame. The holding tanks are directly behind the jack point so be care and don't have a bottle jack slip and do in one of the holding tanks.
A word of caution. These trailers are well built but, heavy and they will roll when unhooked. If there are no wheel chocks, I would be very careful when you get to where ever you will unhook.
I would try the elec brakes if you have the right connector.
I would spin each tire/wheel for serious drag problems and hopefully you can get it home without pulling the drums (short distance ?). Spin the wheel & tire and have someone try the brakes on each wheel.
If you have a considerable distance to go, might be necessary to check grease, although I would think new bearings, races, & seals are in order but, that is a bigger job.