Check the battery terminals and connections before you go replacing the battery.
Take both the neg and pos off the battery, clean the posts, clean the terminals, put them back on, tighten down, then give it a couple days and see if it helps.
The way I'd prefer to test the battery would be get a multimeter ($24 at Walmart,) and check the DC volts when the car is off. Write that number down, then in the morning before you start it check it again, it should be nearly the same or a little less. If it's noticably less (12.6v first reading, 11.6v second) then I'd definately consider replacing the battery.