I believe with the limited info you provided that your GCVWR is 13500#. When you load the trailer, add the W/D hitch, full propane, battery, passengers and misc. weight in the bed you will find yourself at or close to the GCVWR. That being said you will be able to tow it but your comfort level can only be determined by you. Being in the plains states you will probably be OK but heading into the mountains you may be disappointed. If you feel that strongly about the new TT go for it but set your expectations low and suffer little disappointment. Go into it with the thought that you may want to upgrade your TV later and you will be OK. The truck won't fall apart towing that TT but keep an open mind about your expectations and if you wind up not being satisfied don't throw money at your TV for what I like to call snake oil cures since most of the time that solves nothing and just takes money away that could be used to upgrade to a new TV. Good luck.
Doug