I'd have no issues if that were my truck. That being said I'd make sure that I had a good brake controller incase you get into some sway you can apply the trailer brakes for a few seconds to bring things under control. If you have the built in one your good to go.
I wouldn't worry about the weight dist hitch for that one time tow. I might even feel out what it's like and decide if I wanted to drop the coin on a WDH with a trailer that small on a truck that big.
You have to remember at 7 to 8K lbs your truck is very close in weight to the trailer so there won't be a lot of the tail wagging the dog going on.
Good luck and have a safe trip.