Id go with the option of taking it back to the dealer and get them to deal with it. They will have the gear to test it on the spot, and should replace it on the spot. If you find out that the type of battery is not suitable for your use, then thats their fault for not providing the right advice, and they should do the righty by you to keep you business.

I have had this conversation with a few friends, and they all think that a battery is a battery. Not the case.

Traditional Lead acid?
Calcuim calcium acid?
Dry cell?
Gel cell?
Deep cycle?
(plus heaps of others)

They all have differnt specs depending on the job they do.

The calcimum calcimum batterys are good for weekender cars, as they hold max volts/amps for a longer peroid of time without charging, but they fail very suddenly. They come with a 3 year warrenty for cars, and 2 years for commercial applications. They are also a little more expensive.

Lead acids on the other hand, are cheap, have awsome CCA capacaity, and degrade slowly before they finally die. But they can leak nasty acid about the place, need maitaince (usually), and are very heavy and large for the CCA they provide, and prefer reasonally regular charging (ie daily use).

After all that. Take it back to the dealer, be nice to them, plead a sob story, or better send in the girly, and go from there.