EDIT: Just remembered that I have a flash disk somewhere with most of my music on, I'll just back up the rest when I find it, and would it be possible to get my saved passwords from ff and copy it to my phone just in case?
install it on a new partion
if you wish to backup all your firefox details theres a very useful tool ive used many times:MozBackup
it backs ups your entire firefox profile (all bookmarks, cookies, extensions, saved passwords, browsing history, absolutely everything). its extremely easy to use, takes about 30 seconds to make a backup, and then you can take that backup to any computer with firefox, and it takes about 30 seconds to restore a backup. then its just like you were still using the first computer, you would never know you have moved all your data across.