As a Firefox Profile backup method there is nothing better than FEBE.

This will save all your Fast Dial information as well as everything else.

Fast Dial information is saved in Bookmarks.
Recent Versions of Firefox backup bookmarks automatically, but you can also make a manual backup yourself.

However the bookmarks backup will contain all the rest of your bookmarks so is not strictly a Fast Dial backup per se.
You restore the Bookmarks backup using restore function in Bookmarks.

See Bookmarks/Organise Bookmarks/Import and Backup

I hope this answers your question
Many thanks

Good !

Thanks for the quick feedback

Any further questions please let us know...