Welcome to the forum! This is a great place to get ideas and info.
As to the trailer you are considering, I agree...don't do it. Either look for a lighter trailer or a 3/4 ton truck. My trailer is 6200 lbs. loaded except for food, and with my Tundra, I don't think I would want to tow more than 7K max even though the truck is technically rated for more. I towed my previous truck a few times with the Tundra, and it was somewhere between 7,500-8,000 lbs. Although it pulled it ok, I don't think it would be a good combo for the long run. Learn more about payload capacity and how it limits 1/2 ton trucks. Also, dry weight ratings may not include any options such as battery, awning, propane tanks, AC unit, etc. so you have to figure that the dry weight may be several hundred pounds below the actual trailer weight.
For that truck, my suggestion is to look for a trailer with a dry weight of under 5K. That allows you to add 1500 lbs for options and gear, and still be at a gross weight of 6500 lbs. and with a good weight distributing hitch you should be good BUT check all the ratings for your truck and do the math.
Good luck on your search and hope you are camping soon!