Tundra's, as with any truck (half, three quarter, one ton, doesn't matter), are not all created equal. Depending on engine, transmission, 2 wd or 4 wd, cab size, installed options, etc, every one of them has it's own payload capacity. Limited Edition comes with a lot of options and it's payload would be less than other models. Open the drivers door and find it's tire / loading sticker. On that sticker it will have a max weight for occupants and cargo (AKA payload). Then, do the same on the Ram.
Payload gets used up by the weight of anything and everybody that was not in the truck when it left the factory. WD Hitch, anti-sway equipment, and trailer tongue weight are counted as cargo in the truck.
You need a truck with payload capacity to carry the weight of the family, any cargo you may put in the truck, any aftermarket accessories (a bed cap could weigh 200 lbs), and 13 - 1400 lbs of trailer / hitch weight.