First things first, welcome! Lots of knowledge here and lots of helpful folks.
You'll have no issues with power and general ability to tow.
To ChooChooMan's point, you have other limitations. I had an '03 Trailblazer. I believe the hitch is rated for 950# with a WD hitch. What concerns me is your payload. Look at the yellow weight sticker in your driver side door jamb. It will list your payload. It might be 1200# or 1300#. That sounds good until you subtract the tongue weight and the weight of the WDH, likely you're looking at close to 900#, which gets subtracted from the payload. Now you have 300# left for your spouse, kids, dog, and "stuff". You can see that you'll most likely exceed your payload rating.
Moreover, that trailer is a bit large for a GMT360 platform. I had an EXT (GMT370) and I would not have towed anything longer than 20/21 foot. If you have the SWB, that KZ is too much trailer for that truck.