If no warranty you could get the battery load tested for free at a number of auto parts stores across the nation. With newer cars and a lower battery indicator I always suggest having the alternator load tested also. Too many newer cars will trigger a battery warning when the alternator is to blame.
It's not common to see a battery go in under 3 years but it happens. I've even seen some batteries go within the same year they were purchased.
If your referring to red battery indicator then yes it does refer to the battery. Most mechanics just check the battery but in new cars the alternator is typically the issue when this light appears. Most people can realize when a battery is getting low and there car is having a hard time starting. Let me guess though you car starts fine without any type of struggle?
FWIW: I had to put a new battery in my 07 with 50K a few months ago. All is well now. Went with an Interstate. The Honda battery would die just when the doors were open while I was cleaning it. Now I can't kill it if I leave the doors open for a while.