If it is a Firewire device then Disk Utility's info for it will be located in System Profiler > Hardware > Firewire.
However, in my experience Disk Utility will not show the serial number for drives in Firewire enclosures. Drive Genius is one program that can usually do so but its not free.
Is there no way to pop open the case for a look? That would be the most conclusive way to determine the make and model of the disk.