We tow a similar camper behind our EX AWD (3,500 # dry, 4,900 GVWR 400 # tongue) with a weight distribution hitch, anti-sway, and wireless brake controller (Echo). The aftermarket hitch installer had no issues with what we asked them to do and said the car should have no issues. Boy was he right!
The engine and gearbox have no problem getting everything moving, and the braking with the Echo feels like there's no trailer attached at all. We've made three trips so far, about three to four hours each way, and got about 12 mpg while averaging about 65 mph.
The only thing I don't really care for is the high rpms that come with leaving the shifter in automatic mode. Generally, the computer wanted to keep the trans in 5th gear revving around 3,500 rpm. I found that by going into manual I could usually bump between 6th and 7th gear and maintain speed on the flats while pushing some strong coastal TX winds. We had the A/C blasting the whole time and the engine temp gauge didn't change above normal even though it was 95 degrees outside for all three trips.
All in all, I couldn't be happier with how this rig performs. I plan to take the family to Colorado in the next couple weeks so I'll get a taste of how it handles with the trailer at altitude and on some real inclines. I have a feeling it will be no problem!