LOL....I towed a Uhaul trailer that exact same size from Seattle to DC using a Mercury Sable. Moved out there for a year for work....lots of clothes, a motorcycle and other bits and pieces. Other than adjusting my headlights and decreased gas mileage, it had no negative affect on the car.
The ONLY problem I had towing the same trailer coming back to Seattle was when the left wheel came off due to the shop overtightening the wheel lugs, so they all sheered off. It probably doesn't help that since I was driving back in my supercharged Tacoma V6 that I was able to go quicker on the drive back home
Unless you're towing like 15,000lbs, I wouldn't worry about weight distrubition on the hitch, just load it evenly inside the trailer itself so it's not front or back heavy. Everytime I've ever seen a distribution hitch was for vehicles like my F350 when towing some serious weight.
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