First, welcome to the Forum. Sorry for the delay responding.
As long as your other cargo in the truck is fairly light (less than 1,000#) including passengers, you should be okay, but keep it slow! The trailer tires will be MUCH happier at 55 mph than at 65 mph - their max speed.
Check your tires. Max Load on the truck tires MUST exceed the max axle ratings shown on the tire placard on the driver door. Remember, two tires per axle! Make sure they are inflated to this pressure. Check the DATE CODE on the TT tires. Anything over 5 years becomes suspect. These tires "age out" before they wear out.
I assume the TT has brakes. You will need a Trailer Brake Controller (TBC) to make them work. THIS IS REQUIRED!
I had a much older King Cab 4 cyl that I pulled a 2200# pop up with. It did okay, but was clearly a bit underpowered.
Good Luck!