You would need to do SEO again. You never really stop doing SEO as long as you're promoting your site.
Margene is correct. You need to do a 301 redirect from the free domain to your own domain so that you will not lose your page rank. Pages that have been indexed before will remain so. If you do a 301 redirect, then search engines will know to index the pages on your new domain and rank it accordingly. The traffic you on your free domain will be referred to the new one. This is as long as you do a 301 redirect. You can also use the link building service if you want to save time.