First - put the towing capacity out of your mind. You really can't tow that much - I will explain.
Second, in the door jamb of YOUR truck, there is a sticker that shows the Max cargo capacity. That is the number that is important. More options make the truck heavier, so a Limited with have less carrying capacity than a Tradesman. I don't know how air ride effects the number, but the point is that you need to know the number for your truck.
A travel trailer (not fifth wheel) will put about 13% of it's total loaded weight on the hitch. You can find the Max weight of the trailer on a sticker, typically on the drivers side near the front. The empty weight of the trailer is a useless number, unless you tend to pull it that way on a trip.
Lets say the Max weight of the trailer is 7500 pounds. Thirteen percent of that is about 975 pounds. My 2025 Big Horn has a carrying capacity of 1700 pounds. So - 1700-975 leaves me with 725. Add the weight of passengers, the dog, the hitch (100 pounds?) and anything you want to put in the back of the truck. You need to keep that under the 725.
Back to the 12000 tow capacity. Thirteen percent of 12000 is 1560. That means if I want to pull that trailer with MY truck, I could do it if I drive alone, and leave everyone and everything else at home. This is a game the truck, and the trailer manufacturers play. Do not under any circumstances believe the sales guy at the trailer dealer when he says your truck can pull it fine.