I have a towing guide from GMC that lists the max towing weights for all of the GMC vehicles that are capable of towing. I have scanned it in and will try to attach it to this post. If you check the specifications on the BH3410RE you will see that the GVWR is 14,500 lbs. GM lists the 2500HD with a Duramax/Allison 4WD Max towing capacity for a FifthWheel/Goosneck to be 15,500 lbs. As long as you don't overload your trailer you are well within the GM rated capacity for your vehicle. If you check the tag inside your door jam, it will tell you the max load you can carry in your bed. If you are unsure of your vehicle weight you can weigh it with and without the trailer hooked up and that will tell you if you are with in the limits of the load in the bed. But you are well within the GM recommended max towing weight for your truck. I believe that trailer is a great match for your truck.
I had to load the file as a picture, so open it with picture manager and then you can use zoom to make it big enough to see the chart. The top chart is for tag along trailers and the bottom chart is for fifth wheel/gooseneck trailers.
Fred