The only real way to answer your question is for you to take your truck full of fuel, and what you would take with you in the crew cab, people, pets, stuff, and get it weighed front and back axle separately.
With a short box almost all the weight will drop directly onto the rear axle, so take the camper, add 1000 pounds of stuff to it's weight, and see if you have room to carry it with the tires you have.
Remember, adding a hitch and towing anything puts about 150% of the hitch weight on the rear axle, and takes weight off the front.
An awning over the door is nice, and might be all you really need. Campers are high and provide shade because of it. Tarps go where you need them.
Mike