In my opinion, you shouldn't exceed a truck's gross vehicle weight rating (GVWR).
For planning, you plan on a worst case scenario and you look at the trailer's GVWR (gross vehicle weight rating) which is 7,400 pounds. Since it's a travel trailer, you will have a tongue weight of 740-1,100 pounds (10%-15%).
The truck that you buy needs to have available payload for you, your passengers, any add-ons you add to the truck (bed cover, topper, etc.) and anything that you carry (firewood, bikes, foods, coolers, activities, car seats, booster seats, electronics, etc.) in addition to the 740-1100 pounds of tongue weight.
For instance, my wife, two kids (one in an infant seat w/ base and the other in a booster), our truck adds on (hard/roll-top cover) and hitch all weigh about 1,200 pounds. To pull the travel trailer you're considering, we would need payload amounts in the range of 1,900-2,300 pounds.
