First, it's probably too much. Loaded up for a long weekend that will be 8500-9000 pounds with 1000-1100 pounds of tongue weight. You will run out of payload well under that weight.
Start with this sticker on your driver's door. Note what you have where mine says 2051:
Is that where your 1820 pounds came from? Then 7500 dry might be okay.
Subtract the weight of your family in the cab and any cargo in the bed (bikes, coolers, toys, kayaks, firewood, etc.). Then multiply by 7.7 for a good estimated loaded TT weight.
My guess is you'll be happy under 6k dry, closer to 7k loaded TT and even that might put you over your truck's GVWR.
The 2" ball and mount you currently have does not matter. You'll get a new one with the weight distributing hitch you'll purchase, 2 5/16" ball, shank, and bar rated for at least 10k pounds.
