What about the rest of your stuff? Email, documents, pictures, music? I ask because when you get your new computer and start it up one of the first things that will happen after you register the computer is that you'll have the opportunity to use the Setup Assistant. The Setup Assistant will transfer your account from the old computer to the new. It is a convenient option. You'll either need to have the two computers networked - Ethernet cable will be much faster than WiFi - or connect the two computers with a FireWire cable.
However, if the only thing you care about is Firefox - on the old computer, open your user folder and then open the Library and then open Application Support. In the Application Support folder you'll find a folder called FireFox. Copy that folder to the same location on your new computer.