You can do that by using the profile manager. When creating a new profile you have the option to specify a location for the profile folder.

You could create a new profile, then transfer data to it. For details see creating a new Firefox profile on Windows and transferring data to a new profile.

Make sure that you specify an empty folder as the location of that profile because Firefox uses the folder that you specify and doesn't create a new folder in that location. If you create the folder in a location that already has files and decide to create a new folder later then if you choose to delete the old folder with its files you lose all files in that previous location. Firefox doesn't differentiate between files that it created itself and files that are already there when you create a new profile.

Thanks, Was quite easy this way.

Made a new profile on the new location, started FF, closed FF. Copied the files from my old profile over default stuff. Restarted FF and all ok.