Ignore the dry weight. Use the gross weight (GVWR) and go from there. Figure 15-20% of GVWR for your pin weight for a more accurate number because you'll never tow an empty trailer. I'm figuring your GVWR might be in the 13-14,000 pound range with a 2000 pound pin weight, which is perfectly fine for an F-250/2500 to tow. Just for giggles, the pin weight is 3,500 on my 19,000 toy hauler.
2014 Voltage 3600
2013 Chevy 3500 CC DRW
2011 Harley Ultra Limited 2016 RZR 900