I don't know YOUR tundra but I suspect your payload will be between 1500 and 1600 lbs.
fast math forgive my crappy estimates
you and wife = 300 lbs (guessing take no offence)
gear in truck = 300 lbs (doesn't take much in the bed to eaqual some weight. few coolers, bikes, bbq, bags whatever also includes any aftermarket stuff on the truck)
Weight distributing hitch 100 lbs
payload - stuff in truck = whats left for trailer
1550-300-300-100=850 for tongue (not getting into what your hitch or rear axle is rated for)
campers loaded weight x .15 = tongue weight
(remember dry weight means nothing go with campers weight loaded at capacity to account for gear and batteries and propane and what not)
850/.15 - 5666 ish pounds fully loaded ready to camp with water in tanks and propane and everything.
run the numbers with some fluff room for piece of mind and remember if you are touring the country you will not be packed light.
doable YES. don't expect to do it in a giant rolling house. I would think most campers in the 20 foot range would be a good fit.
