Yes, definitely get a good weight distribution unit that has built in sway control. I would think that your Tundra should be able to handle this pretty good. Keep in mind that a 7500 lb trailer will have a tongue weight of up to around 900 lbs. Your Cap is probably a hundred pounds or so. 600 lbs left can be taken up pretty quickly with your weight along with all your passengers, tools, equipment, etc that also will go into the truck and counted against the payload capacity.
I would make sure you have LT tires, preferably E rated. 5.8L?? I thought the Tundra had a 5.7L... anyway, you will have sufficient power..you just need to be aware of the payload and DEFINITELY get a WD w/sway. Equalizer...Dual Cam... and if you really want to get the best that will totally eliminate any possibility of sway, get a Pro Pride or Hensley Arrow.
Good luck
Ron