Once you move to the new domain, simply go into Autotune and the FB App section. Hit the "Refresh" button and that will show you all the updates you need to make. Hit the "Use Recommended Settings" button, and you should be good to go. JFBConnect will do it all for you.
Beyond this, the only thing to be aware of is that any comments or Likes from your old site will be gone. Those are attached to specific URLs, and if you switch the domain, all those URLs will be different.
Hope that helps,
Alex