I towed a similar sized trailer with an 03 Tahoe for many miles, and while I never had any issues with it I always felt like it was on the edges of steering and stopping capacity. I've since upgraded to a 2500HD diesel, and while that is gross overkill for my trailer (I was planning to upgrade that too) I find it way less tiring to drive long distance with, and I get better fuel economy. The main thing to be careful of with the Tahoe is to use a good wdh and sway control, and be very careful not to exceed the rear axle and hitch ratings. It wouldn't hurt to add a transmission cooler even if you have the tow package. I found the Tekonsha P3 with factory adapter harness to work great.
