Yes, you can. I recommend having it installed professionally.
Watch your weights and read the owners manual to figure out the towing capacity of your car. Keep in mind that it's going to take you a lot longer to stop with a trailer then without.
Most cars can do ~1,000 of tow weight, that's trailer and cargo. Again read your owner's manual.
My FWD 5 speed manual Saab went 147,000 miles before the clutch went out. Not all pulling a trailer, but quite a few.
Since your car is FWD, you want nose weight on your trailer, but not an excessive amount. 40 rear/60 nose is about right. Too much nose weight and it will pull the front wheels off the ground. Too much tail weight and it will want to pop off the hitch and make it dangerous to drive. (Not fun when you release the handle and the trailer flies up to meet your face. Safety chains are a must.
Oh, my Outback has the plastic pop-off panels and tow eye in with the spare tire kit.