The number on the chart is a general number. The number on your sticker is for your specific truck with your options as it came off the assembly line. Anything you add to the truck (mods, cargo, people) count against your payload. Gas DOES NOT COUNT against your payload numbers. That is already figured in.
You have a low payload but the only way to get a true number is to fill your gas tank and get the truck weighed. Then subtract that number from the GVWR of your truck.
I just had my truck weighed and my sticker says 1560 lbs but after my mods (195lbs) and myself (215lbs) I only have a little over 1000 lbs of payload left. Thankfully my trailer tongue weight is only 900lbs.
Some will say you can go over your payload as long as you don't exceed your rear axle weight limit. That may be true but that's a call only you can make.
You said a light trailer. Ideal tongue weight is 10% to 15% of your loaded trailer weight (not dry weight). Any more or any less and you'll be at a higher risk for trailer sway.
A 6000lb trailer with have between 600 and 900 lb tongue weight. That means to get that weight you'll have to buy a 5000 lb dry weight trailer. You'll probably have about a 1000lbs of stuff in your trailer. That's the average.
That means you'll probably be looking at about a 23' to 29' trailer. And don't trust the brochure dry tongue weights. They don't include a battery or full propane tanks. Those two things alone will add about 100lbs onto your tongue weight, not to mention your front pass thru will be packed with stuff.
Edit:
I just saw the other thread after I wrote this and you mentioned that you had a 5th wheel. I wrote this on the assumption that you had no knowledge or experience towing. I hope I didn't insult you.