Find yourself an Apple Store, show them the issue, they may replace the battery right there if it's in warranty and the battery is easily removed (unlike the newest line of MacBook Pros). I've had them swap out my battery on an out of warranty machine too.
I believe the basic test for you is:
- Apple Menu >> About this Mac
- Click More Info
- Find the section for power/battery
- If the age of the battery is less than a year and the charge count (cycles) is less than 300, they have often replaced the battery on your reported symptom.
Of course, Apple has a fancy battery testing tool that they will reboot your computer into once you're there in person, so I implore you to find an Apple Store, an Apple Certified tech who won't charge you for warranty repair, or contact Apple Directly about the issue.
For more info on what counts as a "cycle" read this http://www.apple.com/batteries/
Similar issue discussed on Apple's Discussion forums: http://discussions.apple.com/thread.jspa?threadID=1296373