(I Moved your post from another thread to its own).
That trailer is 7,995 lbs dry and has a 3000lbs CCC. Its also 36' long. Big and heavy for a half-ton IMHO. I would advise a smaller trailer.
Your truck is rated to tow 10100lbs but this was before Toyota reduced their caps to correspond with J2807. I believe the 2012 Crewmax can tow a max that is under 10,000lbs. Sometimes significantly under depending on the package
What is the payload cap? As you mention, the payload is part of the problem (with almost any half-ton).
Basically, do not implicitly trust what other owners have done. I tow with a Sequoia and am on the Toyotatundraforum site occasionally. Its shocking what some of them do with their tow setups. Way overweight but a few insist to high heaven that this is the best towing setup possible
You need to do the math and the calculations with a setup this close.
Your trailer is going to come to you weighing close to 8,400lbs from the factory and then you are going to load your cargo into it. Assuming cargo, a little water, battery(ies), and propane, I bet this trailer weighs in at well over 9,000lbs.
At a minimum of 9,000lbs, the tongue weight will probably be 1,200lbs. Not many tow with the TW at 10%. I find 13% to be good for my setup. You may be between 10-15%.
So, those are closing in on your max for GVWR and maybe your payload once you count your passengers and what you plan to carry in the bed of the truck. So, I encourage you to use this calculator to verify things for yourself.
Travel Trailer Weight Calculator