A poll on here determined the average RVer adds 1200 pounds over manufacturer dry weight. Families and full timers add more, while 1-2 people on short trips add less. Also, many manufactures do not incldue optional equipment and mandatory optional equipment in the dry ratings. My TT came in at 300 pounds over the brochure weight for example.
So, 6k dry, you should plan for 7k loaded. That's really close to your tow rating. What axle ration do you have? How about payload per the tire and loading sticker on the driver's door? With a family in the cab, some camping gear in the truck bed, half tons usually run out of payload to also support 900+ pounds of tongue weight.
7k loaded TT is about the happy top end for most half tons. If you have 3.55 or 3.73 axle, then you should be okay. Tow in 3rd gear on the highway. Use Tow/hail mode if available. Expect to slow down on hills and kick down to 2nd gear at 3500-4500rpm occasionally. Get a WDH with integrated sway control. Enjoy camping!