Transferring a Firefox profile from one computer to another can be a pain if you have to do it manually. Sure, you can locate the firefox profile directory and then copy it to the new machine, but then it doesn't automatically show up in the list, etc.
A much easier method for backing up and restoring profiles is to just use the MozBackup application to backup and restore the profiles to a single backup file.
When you launch the application, you can choose to either backup or restore the profile. You can choose which profile to back up, and what file to save it as.
You can restore the profile on another computer by simply launching the MozBackup application on that computer, and then selecting the profile to restore to, and chosing the backup file that you copied from the first computer:
It's really as simple as that.