Not sure I understand your question exactly.

1.
I would recommend if you are moving to a new computer to use FEBE and simply move the complete Firefox Profile from computer A to computer B.

This Will include automatically all Fast Dial Information.
The new Firefox Profile will be a copy of your present Firefox profile.

2.
An alternative would be to make a backup of your present Bookmkarks in Organise Bookmarks, and then load that backup into your new Computer.
The bookmarks backup will contain your Fast Dial information.

Obviously you will also need to load the Fast Dial extension separately.

Many thanks