It is my opinion that the easiest way to migrate the Fast Dial Profile is to use FEBE and simply make a Full Profile Backup from your present working Fast Dial.

This is a full Firefox Profile Backup so will include every aspect of your Firefox Profile.

And then make a Full Profile restore to your new empty Profile.

It is worth remembering if you are moving to a different Computer that FEBE makes a Full Profile Restore from another Profile to the one that one wants to restore.
So you may find it necessary to have two Profiles running to facilitate this. One profile to run Febe and the other to Restore your backed up Profile into.

If you do a FEBE Full Profile Backup and Restore, this will mean that your images stored in the Fastdial Folder and your settings stored in Bookmarks will all be effortlessly restored to your new Profile by FEBE.

FEBE
Userlogos Tutorial

Download

See also FEBE Documentation
link 1
link 2

Go the New Profile, open Firefox and the Fast Dial Page will open as it did in you previous Profile

This is very labour saving and gives a very satisfactory outcome.
This software is rock solid and easy to use.

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This is the more traditional method of Migrating your Fast Dial Profile in Fast Dial Version 2.x

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In Fast Dial 2.x running in Firefox 3.x all Fast Dial Settings are stored in Firefox Bookmarks.

That is your Page and Folder Information, your settings and the URLs

But NOT the Logos which are stored in the fastdial folder in the Firefox Profile.

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It is useful to understand that the Fast Dial Folder in Bookmarks cannot be backed up and then restored in isolation, and that it is necessary in order to migrate the Fast Dial Folder to migrate the whole of Firefox Bookmarks.

So backing up and restoring of Fast Dial 2 is more a Firefox function than a Fast Dial Function.

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1. Backup your Firefox Bookmarks

You will need to go to

Bookmarks
Organize Bookmarks
Import and Backup
Backup function.

Backup your Bookmarks to a place of your choice.

2. In the Firefox profile in which you wish to load your Fast Dial settings, go to:

Bookmarks
Organize Bookmarks
Import and Backup
Restore function

and restore the file that you had saved in 1.

This will among other things restore your Fast Dial Folder where all the Fast Dial information is stored.

3 Once this is done and you return to Fast Dial, you should re-discover the Fast Dial Profile that you have just moved,

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Another way to migrate your Fast Dial settings in Fast Dial 2.x for the more technically minded is available here.