Weight-wise, I'd say you are fine. That set up matches mine almost exactly and I've done about 3,500 miles over 15 months in mine with no issues. Only thing I couldn't comment on would be the altitude since I haven't had mine over about 1,800ft. The only thing that might be above my comfort zone in your set up would be that length. We started off looking at a 27 and ended up deciding to drop to a 21 for now. Partly due to the ratio of trailer length to car length and the chances of sway, and partly due to the fact that we were coming from a pop-up, and I was a little skittish of the jump from 12ft to 27.
I use a Reese Strait-line hitch (combined WD and anti-sway) with a P3 brake controller and ended up adding the Airlift 1000 to raise the butt a bit. I love the setup and feel very comfortable with it.
Now, I have to ask, what TT did you fall in love with? We're already starting to shop around for our next TT, but know it will have to wait until I get a truck since the weights will be a little higher. For now, Our favorite is the Resort 249BH. Looks nice and has the features that we absolutely want to make sure we add next time (walk-around Queen, bunks for the kids, and a slide-out).