Your math is right but as kohldad explained, it get's more complicated than that.
Weight the truck at a quarry, landfill, scrap yard, feedmill, or truck stop. Try to have it full of fuel and any passengers and pets that you will take with you camping. Subtract the scale number from the 9,200 GVWR and then you know what else you can add.
Going beyond the GVWR is quite common when hauling a TC. For better or worse I'd be 75% of trucks hauling TCs are over their GVWR. It's quite common to go by the rear axle weight rating (RAWR). So, when you weigh the truck get separate axle weights. Subtract the rear axle weight from the RAWR and most people would say you can haul that much. It may or may not be much different from using the GVWR.
After that, you can get into a whole discussion of how the tires really set the RAWR and if you upgrade the tires and possible even wheels then you can haul much more weight. This typically leads to air bags or helper springs on the rear, heavier duty shocks, anti-sway bars, etc.
I've hauled my TC on a truck with a GVWR of 9,900 and the rig scaled at 11,150. I currently haul it on a truck with a GVWR of 11,400 and the rig scales at 13,100. I've got thousands of trouble free miles with both trucks.