Ignore the tow rating. Your truck's rear axle and GVWR will be greatly exceeded with a 9900 pound TT, a family in the cab, and the a bed full of camping gear.
This is tthe math on what
1200 pounds of payload
500 pounds of people in cab and stuff in the bed
700 left for TT tongue weight. That's about 5500 pounds loaded travel trailer, and 4500-5000 dry.
If you, wife, and kids are only 300 pounds and the truck bed is empty, then you have 900 pounds of TW which is closer to 7000 pound loaded TT.