You should have no issues.
I say this as I have a 2005 Chevy Colorado with the 3.5 I5.
And the trailer you listed is about the same as ours.
I have been towing for 4 years now and live in British Columbia Canada and have gone through many mountain passes here with no issues.
Just remember that because you are gas and the power bands are in the higher rpm range that when it down shifts on a hill it will rev up. All is ok.
With 3:73 gears in my own truck I run 3rd gear at 2800 rpm at 61 mph. And I have my cruise control set.
Going up big hills the truck will down shift to second gear and then maintain 61 mph and run about 4300 rpm. And still not kick out of cruise control.
2006 chevy colorado xtream.
Holiday Rambler 187qb.