Launching another Firefox window is easy, just drop-down FILE tab and
choose "New Window". I'm now using Kubuntu 11.10 and am not yet happy
with it.
I hope it would at be at least this simple under Unity. Changing
desktops under KDE is not nearly as clean and simple as Gnome was. On
the old machine
(Ubuntu 11.04) I'd just change desktops and open a new instance of
Firefox.

Another Firefox issue which I have not yet resolved is how to get my
Bookmarks over on the new machine. They've taken out the Backup/Restore
from dot json
file in Firefox. If I have to sit two machines side by side and
manually transfer all my bookmarks it will not be easy. My previous
machine Gnome/Ubuntu 11.04
made this a simple process. I just returned from a Thanksgiving week
vacation so have not yet read all the traffic about the Bookmark
backup/restore issue. I
hope someone has an easier solution.