There is no way I would worry about hauling that weight/trailer around with a stock 3/4 ton.
The OP is not talking about living in his unit and towing it all over Gods creation for the next decade. He is talking about recreational use. Since his truck nearly has the capacity to haul that unit on a full-time basis it is certainly up to the task of doing it on a recreational basis- and quite safely.
Finally- We all know the mfg's build warranty claims costs into how they figure weight ratings. A few hundred pounds is not going to make any difference.
To the OP- go tow the trailer as your truck currently sits. You will quickly decide whether or not you feel comfortable. If you don't feel comfortable- don't buy the trailer. If you do feel comfortable- buy it and add some airbags to your truck. The airbags will help with ride comfort and load control- They made a giant difference in my last three trucks!