I'd agree with keymstr. I had a Chevy 1/2 ext cab 4x4 SB max tow 9700 payload 1650 pulling about 5000 TT. The payload was over by 150 lb when I started that trip and dropped off a few items later so I was back just under payload. That set up pulled well, wasn't white knuckle and would get up and go when needed.
Here are some figures I found on a forum. As mentioned above you can find your truck specs.
2WD Auto w/3.73 - 7,100
2WD Auto w/3.42 - 6,100
2WD Man w/3.73 - 5,100
2WD Man w/3.42 - 4,100
4WD Auto w/3.73 - 6,800
4WD Auto w/4.10 - 7,800
4WD Man w/3.73 - 4,800
4WD Man w/4.10 - 5,800
The maximum GCWR varies from 9,500 - 13,000.
Just say you are at 7,000. You may be able to pull it but the issue is do you want to. If that truck is at max or if mine had been at max it it would be pure heck to drive. I couldn't imagine pulling 7000 with the Chevy I had but people do it. It depends on how far a person is going too. If you are doing this full time you want it to be comfortable and low stress. Also remember that the numbers they give will only include iirc a driver of about 150 pounds. All passengers, dogs, fuel and everything else have to be subtracted. Dont believe anyone or any sales people, believe a scale weight. Weigh after you set up your rig so the tongue weight is correct and you are safe before hitting the road.
Some websites will have people arguing that they tow at max all the time and there is no problem blah blah blah. Again, there is a big difference between what you can pull and what you will want to pull. The risk you are up against is setting this all up and being unhappy with it. If nothing else beg borrow or rent an expected weight of trailer and see how it pulls. A utility trailer is not going to duplicate the frontal area of a TT. It sounds like a pita but you are putting together a long term living accommodation not just keep your kid happy by taking him to a local campground now and then and then parking it all. It can seem daunting at times but you just have to work through it. If you had a one to or 3/4 you have a huge variety of rigs to choose from. When you have a minimal tow vehicle you have to make compromises.