I would get a Reese dual cam or equalizer wd/sway control system.
I've been pulling upwards of 8000 with no bars, with my 2014 new to me in late February with a V6, 6sp auto and 3.42 gears. The 8000 trailer was a literal small cement mixer with 1.5 yds of concrete in a rotating drum. I pulled a 3%grade in 4th, 1.05 direct equal at 55 doing 3500 rpm. You have another 50 ponies plus, along with at least 50 lb ft of torque than me. First gear is a 4.3 for you vs my 4.10 in trans. I believe gears 1-5 are closer spaced than my 1-4. Top three in both trans I believe are 1.05, .85 & .65.
I recently went to 285-65 tires vs stock 265-65-18 tires, gained 1" diam, reduced effective ratio from a 3.42 to about 3.23 like yours. I'm not going to say no difference. A lot may have to do with the tires being 10 lbs per heavier. I'm sure the effective ratio Change is part of the little slower to get going, lower mpgs.
I would not worry about pulling that trailer with your 1500. I'd pull it with mine.
Marty