If you have 1000 lbs left over, 10 percent gives you a 10K trailer.
It is likely he will have nearl 1000lbs of payload left over given the current occupants of the vehicle, but there is NO WAY he would ever be comfortable towing a 10,000lb trailer with that truck. Driving would feel heavy and sluggish, with frequent down-shifting.
Not to mention, 10 percent is the absolute minimum. Most travel trailers run anywhere from 12-14 percent tongue weight.
If you start with a trailer around 5000lbs empty, you will have plenty enough to tow once you've loaded up to go camping. That puts the trailer at between 6000 and 6500lbs with options, loaded and ready to camp.