Hi and welcome to the forum. You will likely get a lot of opinions and various experiences on that subject. From my personal experience: Towed a 6000# scaled TT with a fully HD equiped with tow package Tahoe for years with no issues about 50k towing miles. I would characterize the vehicle adequate for that job. It was an '05 with the 4 speed auto. The newer 6 speed autos would be be better.
Since you are getting a new (to you) tow vehicle I would recommend just go ahead and get a 3/4 ton based tow vehicle with the tow package. Don't need diesel for that wieght but if you get one it will make a difference in towing comfort.