I tow 8,000 lbs. 24 ft. equipment trailer hauling a Kubota Diesel Tractor with Bush Hog or multi-gang disk. All tractor tires are filled with water for stability and a bunch of weights are hanging off the front of the tractor.
The trailer is a HD double axle (rated for 8,000 per axle - 16,000 total) with brakes on both axles and is controlled by a Prodigy controller.
I tow without any problem, but don't tow very far. It's only about thirty miles at the most each way.
But from what you are saying my main concern will be weight on your rear tires (tongue weight and weight inside your vehicle) and total gross weight. If you have passengers and a load in the back of your SUV, you are probably go over the safe limit.
My second concern is whether you will have any rear suspension travel left. With my load, the air shocks level it out, but there is just about nothing left.
So, I would have doubts about a cross-country run, and would be worried if I had passengers and gear on board.
It will probably do the job, but you would want to hopefully run on relatively flat terrain, stop frequently and not drive much over about 60 mph.
Of course, everybody has a different philosophy about towing. I see little midsize pickups towing incredible loads without any obvious problem, but I don't know how long they can do that without tearing up.
But if watch your gauges, keep everything in normal operating temperatures, don't overload your tires and don't get in a hurry you can get by.
I'm sure there are those here who would disagree with me, but you are right at the border of needing a 3/4 ton diesel if you are going to pull that load regularly at highway speeds.