You should have no problem.
I pulled my 18' Rpod with a 2015 Ford Escape with the 2.0 Eco boost engine. Tow capacity was 3500 lbs. Even before I installed a 7-pin socket, electric brake controller and a weight distribution hitch I had no problems at all.
The electric brake is required in most states and it just makes sense to have it. You might be the best driver in the world but if another driver screws up and puts you in a position to stand down on the brakes you'll be darn happy you have it!
The weight distribution will eliminate the possibility of "the tail wagging the dog". A very frightening experience I assure you!
If you chose to install the brake controller yourself consider the following: follow the manufactures in structions and install 2 30 amp fused relays. One for the controller and one to power the refrigerator in you trailer when towing. Otherwise your on board battery may go flat by the time you get to your destination. Same with using propane.
I'm rather fussy and took the time to route all wires up through the interior of the car. Placed the fuses on the radiator support crossmember near the battery. Then followed instructions and adjusted the brake bias untill the brakes locked up, then backed off a notch.
The weight distribution system was a bit more physical labor and I had a RV Dealer thighten the hitch ball to the recommended 250ft lbs.
Happy camping!