i would clone/copy over my entire OS (using SuperDuper) onto your external FW drive, this way if you ever need to use your installed utilities and/or need access to files in case of an emergency, you'll have them at hand. You'll also benefit from a bootable clone.
If room allows on the external, you could partition the drive into two and also install a clean and up-to-date version of your current OS. Once installed, boot off this volume, update it, if required and migrate your settings and preferences, from your internal drive so that you will not have to deal with setting up again and all your passwords and such are in tact.
A third option which I've done in the past is to install a minimal OS onto a FW partition and add a few utilities like Disk Warrior, TechTool and the like, leaving some room to recover files but offering me a complete suite of tools and a bootable volume to work from.
To answer your question, yes, boot off the install disk and then install on to the Firewire drive. Plug in the external drive, make sure it's properly partitioned and formatted beforehand and then reboot from the install discs to continue installation.
If room allows on the external, you could partition the drive into two and also install a clean and up-to-date version of your current OS. Once installed, boot off this volume, update it, if required and migrate your settings and preferences, from your internal drive so that you will not have to deal with setting up again and all your passwords and such are in tact.
A third option which I've done in the past is to install a minimal OS onto a FW partition and add a few utilities like Disk Warrior, TechTool and the like, leaving some room to recover files but offering me a complete suite of tools and a bootable volume to work from.
To answer your question, yes, boot off the install disk and then install on to the Firewire drive. Plug in the external drive, make sure it's properly partitioned and formatted beforehand and then reboot from the install discs to continue installation.