We tried once (home from the dealership) with a Sienna (3500lb towing capacity), but quickly decided to upgrade to something larger. We ended up with a 2011 Dodge Durango with a 7200lb towing capacity and it is more than enough for a family of five and the 176t. You should be fine with the Pathfinder and 6000lb capacity. Does it have the factory tow package? You will probably also want the weight distribution hitch if you don't already have one. A sway bar might come in handy, too, if the Pathfinder doesn't have anti-sway built-in. If you're not sure, just do some conservative math with your weights and make sure you are under the trailer load limit (about 1100lbs), your GVWR, and your GCWR, which is the combined weight of everything. I think the Pathfinder is over 11000lbs so with the weight of the vehicle and trailer (~4600lbs + ~2700lbs) that leaves you over 3000lbs for people and other stuff. Lots of headroom!
Have fun!
Mark