A few comments to the original poster: I tow with a Frontier ( 2006, 4WD, CC 4.0L V6, six speed manual ) and also with a F350 diesel dually.
The camper I pull with the Frontier is a 19' funfinder, that weighs 4000 pounds ready to go. My comments are these:
1. you "may" be within the limits of your truck with your camper, and you likely "can be", given proper loading and choice of "things to take vs things to leave home". You will need to go to the CAT scale to determine this.
2.You'll want to arrange things in the trailer with some of the heavier items over the trailer axles, and/or in front of the axles. Shoot for a tongue weight of about 12 to 13% of the actual weight of the trailer.
The factory receiver hitch has a stated weight limit of 650 pounds, however, this hitch is actually a Curt hitch, that is rated at 800/8000. A guess would be that Nissan states 650/6500 to make the numbers match the rating of the rest of the truck.
3. Set your WD hitch up to achieve 100 FALR.
4. Your automatic transmission is a good one. It is the same trans that is in the Titan, so it is effectively rated to tow over 9000 pounds. The small cooler you see in front of the A/C condenser is not a transmission cooler. It is a power steering cooler. The transmission cooler is integral to the engine cooling system radiator.
5. If towing a lot, I would change the transmission fluid and differential oil on the "severe service" schedule. It's in your manual. In the diff, use only synthetic oil ( specified in your manual ).
Those who are making comments about the Frontier being inadequate in your case are guessing. Going to the scales takes the guesswork out of it. A properly setup Frontier is a nice tow vehicle for trailers within it's limits. I've towed two different trailers with mine over 30K miles in all conditions.
Have fun camping and enjoy your truck and trailer.