If the trailer has surge brakes, it won’t need a brake controller.
Don’t forget, when considering GVWR and towing capacity, if you get a weight distribution hitch and a sway control device, you will need to consider the weight of this additional gear and add it to the trailer’s GVWR and tongue weight.
A trailer this large probably has more than one axle.
That V-6 would really be wheezing trying to pull that much weight up a 7% grade at high altitude and it’s not something I would want to do. A lot of people that are stacked up behind you will probably make various gestures and refer to you by colorful names when they finally get an opportunity to pass. 
A V-8 gas or diesel rig is preferable.
Even with 2 axles, the tires tend to be small. You have to be meticulous with tire pressure. I bought a compressor to carry with me because the pressure would change depending on altitude and climate. Also its hard to find air on the road. If I were to RV again, I would go with a motor home or a fifth wheel with one of those big rig haulers. With about a 500 gallon gray water tank.
That’s great for you, but the rigs you would want would be a lot more expensive than what the OP is considering. What you are proposing would cost between $70,000 and $200,000. The trailer the OP wants probably costs between $8,000 and $20,000.
All the responses have really helped me. I want to thank everybody that responded. One more thing, the saleman trying to sell me the trailer was more than willing to put me in a bad deal (truck to small for the trailer) just to earn his commission. I am happy that I investigated this matter more, something did not seem right to me.
Thanks
That 3225 lbs limit you mention makes sense based on what I have experienced so far. Currently I tow a pop-up trailer that weighs 3,000 lbs. I have often climbed a long steady mountain going west from Yuma Az to SD Ca and have noticed that even at this weigh it takes some work on the part of that V-6. But like I said, I am on a budget and I was hoping against hope.
Thanks for the link to the hitch site. This info is great. Thanks you so much.
I just want to make the point that trailering is not as casual as it seems. After you see a few destroyed trailers along the freeway with folks belongings strewn about; after you’ve had a few blow-outs and near fires; after you’ve burned out a few trannies and rear axles, the added initial expense of a heavy duty unit seems like a deal. I think that is what sold me on the Hensley, because it added significant control over the rig, although it was bothersome to hitch and unhitch.
You might seriously consider buying a small light weight trailer like a Casita. Not spacious but well appointed and your weight issues will vanish along with wear and tear and bad gas mileage.