You're always better off selling your car yourself instead of trading. Trade-in value is nothing but the wholesale(auction) value of your car. The problem that comes up GtoRA touched on. If you owe more than you can sell it for you have to pony up the difference to pay off the loan. The claim that dealerships make that they will 'pay off your loan' is just a gimmick. That money is profit that they are giving up to show you more money for your trade and can be used as savings to you. IE, they sell you a car for 20k, and give you 3k more than the trade value of your car, which is just enough to pay off your current loan. With no trade, that 3k can come off the 20k, so you pay 17k instead of 20k.
In short, sell it yourself. With only 9600 miles on it you should be able to sell it quick, and it could probably bring anywhere from 11-14k, depending on equipment.
Holler at me if you have any questions, I'm pretty familiar with the process.