I think that is a nice combo. You will have about 500 pounds to work with inside the GC, (pending the fluid levels) take out the wife and your kids so you can do the Math on what how much you can load in your SUV. As far as wagging around, you may always feel something from the big rigs and fast SUVs in the left lane, but it will not be unsafe as long as you maintain your weight. The TT is light, just the payload as you mentioned, put as much as you can in the TT and you will be good.
What kind of WDH hitch did dealer install, (they are not all created equal)The GC is a nice SUV and a very capable TV when used correctly, you should not have a problem.
Congrats and have fun!