A superb program called MozBackup packages all your essential Firefox and Thunderbird settings: Bookmards, mail, contacts, history, extensions, cache etc. Download the program MozBackUp.
Install the program and run it. Pick your Mozilla program and your user and choose "Backup a profile". You will be able to password protect your backup file. Please note that you can't run Firefox when you're backing up. When you're done, the resulting .pcv file will contain all your settings. Email the file to your account and download it on your new computer. Install MozBack Up in your new computer and now choose the option "restore a profile". This should set your Firefox in the same way you had it on your old computer.
And finally my friend Kenxu has give me a tip on how to Backing up Bookmark in Firefox :
Here is the link : http://www.mysites-advisor.com/tips_to_backup_firefox_elements.txt