2014 Cherokee Grey Wolf 29BD and Toy Tundra V8 5.7L

If you already owned the Toyoda I would agree with the posters that say it can be done which it could with careful weight management. But since you are getting a new truck to tow with go get something that will easily do the job and make your towing experience pleasurable. For that trailer get a 3/4 ton, your choice of brand and engine. It's a little (and I mean a little) overkill but will get the job done with no problems.

Looks like tongue weight will end up being 900-960 pounds and payload seems to be around 1500 pounds. So depending on the weight of the family and put most things in the trailer rather than the truck you might be good. Wheel base vs the length of the trailer you should look into but other than that be safe and have fun.

We own and tow with a 2013 Tundra. That trailer is about 34 feet long with a tongue weight of 753lbs. That is too much trailer for a 1/2 ton truck. Sure it will pull it but not in a safe comfortable manner.

I tow a bigger TT than that with my Tundra {2008) and it does just fine. Go for it!

Tundra is a great truck, just ensure it has enough payload. If it do not, shop around for a TV that has more payload then you think you will need

I'm not Toyota bashing. My wife's car is a Toyota and it's the most reliable vehicle I've ever had.
However, I would get a truck with more payload.
By the time you add up the tongue weight of that trailer fully loaded, your weigh distributing hitch, all the passengers in the truck, firewood, grill, cooler, bikes, tools, dogs, etc. You will probably pretty much be maxing out the payload rating on the Tundra.