Have you tried using Finder's burning capabilities? If that works, then I'd say there's something funky going on with the software.
If not, since you bought the machine at the end of January, you could always take it to an apple store or certified apple repair center and see if they can repair/replace the drive. Since it's still under warranty, the repair should cost nothing to you. As far as an ETA for that sort of thing goes, I honestly couldn't give an estimate.
They likely would not just give you a new or refurbed machine, since it only needs the superdrive replacement. They typically only do that if the machine is too costly to repair or if it's been in for a lot of repairs. Plus, afaik, the stores don't carry refurbed machines in stock.
Another option would be to get yourself an external drive, which can be had for about $40 if you look in the right places.