If the OP was in washington state, he would take his tare of 63xx, lets say 6400 time 1.5 or 9600 to the next highest ton. And HAVE to buy a plate for 10K lbs, That would be his true legal gvwr per the LEO's and how the wt laws are enforced here. So his legal payload would be another 1000 lbs higher than the door sticker.
MOre than likely, he will be fine, but he will be near limits of the truck per say. I personally do not like to tow trailers over 2 to 2.25 times the grawr. So if it is 6100 lbs, 12200 lbs of trailer. Could get up to 13 to 13.5K lbs.....then the tail starts to wag the dog per say. Even if Dodge had a lets say 16K trailer limit, I would personally still limit my self to 12-13K lbs of total trailer.
marty