Hard drives can and do go bad at any time. In my experience they usually last a good long while, but occasionally you'll get a bad one. The bad ones can fail at any time no matter if they are new or old. Those kind of utilities do sometimes give false positives though so you might want to get a "second opinion" with other software diagnostics, or repeat runs of the same one.
Since your machine is new, the hard drive will be covered by apple so I would recommend you take it in to the apple store and let the techs run their own diagnostics. They should be able to confirm or deny the problem. If there is a problem then they will repair it for free (assuming you haven't already voided the coverage somehow).
If that's not an option then you could just replace the hard drive yourself. They are pretty cheap these days and in your model it's easy to do yourself:
MacBook Core 2 Duo Hard Drive Replacement
If that doesn't appeal to you then you could take a more cautious approach. Keep your data fully backed up all the time, and regularly run the diagnostic to see if the problem seems to be getting worse, all the while keeping an eye out for other problems like random crashes. If it's clear that it's dying then just replace the hard drive.