Well, I agree with corkyg's recommendation to back up right away to be safe, but you should NOT need to restore the array data after it is rebuilt. The RAID systems I've seen do exactly what alyarb anticipates. Once you install (physically) the new replacement drive you follow the boot screen prompts to enter the RAID management screens. There you add the new drive to the failed array and tell it to rebuild it. "Rebuild" INCLUDES making a complete copy of all data from the older good drive to the new one so that the array is completely restored. That painless recovery and rebuild from one failed drive is the advantage of RAID1 over RAID0.
In buying the replacement drive, choose one that is exactly the same size as the old one, or a little bigger. It MUST make the new array member the same size as the other. Although it MIGHT be possible to use a much larger drive and create a non-RAID Partition in the Unallocated Space it leaves, I really don't think that is a good idea. So waste as little space as possible and make the new one at least only slightly larger, if not an exact match.