To start out, if you have the Pilot already, use it. It'll do okay with a popup. Just slow down and shift down for long, steep grades in either direction.
Get a brake controller, assuming the popup has brakes. If not, it's possible to add them (look for a square backer plate with mounting holes behind the wheel) or to replace the axle with one that has brakes. Definitely important in the mountains.
I towed a 16' TT through the Rockies a couple of times with a 270 HP V6 Toyota Highlander. It worked well enough, but then I didn't push it hard.
Go have some fun! After you've used the popup a couple of times, you might have a better idea whether you want to stick with what you have, or upgrade the tug or the trailer or both.