I would get the battery checked. I would go to more than 1 place though...all motor accessory outlets and fastfit places do free battery checks. You say new alternator November 2011??? which is in last 7 days? I have only done 3,500 miles in last 18 months. 800 miles in 1 week should not result in flat battery unless you have a serious drain or a totally knackered battery.
sorry dave 1 alternator was fitted in 2010 not 2011.i only use the car about once or twice a week doing aprox 6 miles each time.