Dave, you are going to find payload capacity an issue. 2016 Tundra max towing is 10,500lbs, which is also going to be an issue if you really weigh in at 10k. I bet you find ure close to 8500-9k.
While payload is not a legal number if you go over, not going to be fun. Trailer weight is a legal number. Minimum tonuge weight should be 10%, so youre looking at 900-1k lbs already. Throw in the family and other inside cargo and you only have 100-200lbs left in bed. Not a Toyota problem, its a 1/2 ton vs size of camper problem. Can you do it and can the truck do it, yeah. But its not fun and you wont be winning any races or keeping components from being overworked. No worries if you are only going to haul it a limited amount.