IMO that vehicle may be able to pull the 6500 lb trailer but you most likely will be over your weight limit of the axles once you load up..
So load 4 people, gear, and tongue weight of say low end 650 lbs..
So now going down the road at 60 mph with the family in the car the rear axle gets hot and welds itself together or breaks suddenly.. That could be catastrophic...
You cannot overload the vehicle.. I guess best you can do is get the payload rating off the door tag and post back here.. Thats paylad not trailer towing capacity..
Last I am in monmouth county. I would pass on that vehicle IMO.. I would be looking at 4 door pick ups if you are serious about towing a 6500 lbs trailer with the family...At least 3/4 ton...