First - the DNS-323 is not particularly sensitive to power failures (and I speak from experience) - you just caught a bad break.
Second - the DNS-323, with firmware 1.06, supports UPS monitoring through the USB port, so you can shutdown safely in case of an extended outage.
Third - based on what D-Link says - the disk configuration is stored on the disks, so you can move the disks to the replacement unit without losing data - I have not personally verified this.
Last but by no means least - you can connect one of your RAID1 drives to a Windows system with ext2ifs loaded and get access to the data. I would suggest you do this and backup the data (if you don't have a backup already) before proceeding.