I had a 2013 Tahoe with 3:08 rear end gears and towed a 6,200 pounds dry 31' TT. Dealer lied to us and said it had the 3:42 rear end gears and full tow package. The Tahoe towed the TT up both sides of the Grapevine (I5) without a problem at 45 mph. I did add a transmission cooler and Firestone air bags to the Tahoe to help keep transmission temperature down (worked great), the air bags to help with the load.
At your trailer size and weight you should have no problem towing your trailer.
The Tahoe that comes with 3:08 rear end gears do not come with a transmission cooler, larger radiator, oil cooler lines and heavy suspension. The Transmission cooler and air bags were easy to install. Changing the radiator and rear end gears was impossible.