That is likely a good combination for you. Take a look this sticker on your driver's door. Note what it has where mine says 2051.
I'll start with 1500 pounds. Take away 600 for people which leaves about 900 for trailer TW. That would be plenty for about 6500 pound loaded TT such as the one in which you are interested.
Please verify you have the 3.42 axle and HD trailering equipment which changes the tow rating from 6400 to 8400 pounds. Even if you do not plan to exceed 6400 pounds, towing any high walled trailer is a lot of work for your engine and transmission so you will want the higher capacity transmission cooler in the trailering package. Use tow haul mode whenever the trailer is connected. I also prefer GM's "Manual" mode which limits to gear. M4/M5 are likely appropriate.
Get a WDH with integrated sway control and learn how to adjust it. If you do not have the OEM integrated brake controller, get a proportional one such as Prodigy P2/P3.
