The ignorance of replies is overwhelming...
There is simply not enough information to make an educated decision here.
What model Tundra, what is your payload rated for?
The weight of the trailer, is that dry or gross?
What is the gross tongue weight?
How many people will be in the Tundra, how much gear will you pack in the bed?
The Tundra is a great truck and can easily handle up to the max payload rating. I'm sure it can handle substantially more than the max payload, but I don't encourage people to exceed there ratings.
A 2wd reg cab Tundra can have over 2000 lbs payload, a 4wd Crewmax can have as little as 1340 lbs payload. My Doublecab 6.5 foot bed 4x4 with the 5.7 has 1640 lbs payload.
The trailer might be gross weight at 7800, which means tongue weight of 1000 lbs. Figure 100 lbs for a good WDH and you are around 1100 lbs.
If its 2 people and a couple dogs, the Doublecab will have 500 lbs for the passenger, dogs and any gear.
OP, do your homework and check your numbers. If the math says the Tundra can handle it then you will have a great tow vehicle. I love my Tundra, it tows great and handles the weight with ease. Plenty of power, comfy, always feels solid when towing. If the weights are too high, you need to step up to a bigger truck.
If you do find that the numbers work for your Tundra, or any other 1/2 ton vehicle, I would encourage you to look closely at your tires. Most 1/2 tons come with car tires or weaker truck tires. My Tundra has E rated 10 ply tires which certainly helps it feel more stable. Towing a 30 or 31 foot trailer is right at the maximum length I would ever consider with a half ton. D or E rated tires will go a long way in making your tow vehicle feel more "planted" going down the road.
Good luck and be careful about the advice you get on the internet. A lot of people talk/write without really knowing what they are saying. Some of it is ignorance, some is stupidity, some is blind brand loyalty. You need to do the math yourself with real world numbers and make a decision based upon the facts.