Keep in mind this trailer will be somewhere between 11,500 and 12,000lbs loaded and ready to go with >2000lbs of pin weight. Yes you will put that much stuff in it, and options like AC and propane are not included in the dry weight.
The truck certainly has the power, and you are not going to exceed any axle ratings. However, you will probably exceed the GVWR of the truck, and you have to decide if that is an issue for you or not.
Factory GVWR is not a legal limit in the US at this time, so you will not get ticketed, or denied insurance coverage should there be an accident. People might try to tell you that to scare you, but there are simply no verifiable accounts of it happening. With an RV, if you look good the cops leave you alone.
The truck's not going to collapse in on itself the moment you go 1lb over any rating, but there may be some long-term effects on the truck such as extra wear and tear if you travel often. One thing you will probably want to add is airbags to take some of the sag out of the rear end when you're hitched up.