Hey SG,
Just covering some background stuff before answering you questions - for anyone else who might be wondering whats happening here?
If I understand correctly you are redirecting one domain to another domain, where the directory structure and the files are identical.
The best way to redirect incoming traffic is using the 301 redirect - which is the most SEO friendly method.
Put this code into a .htaccess file, and upload it to your "old" domain root, and it will redirect directory for directory, file to file to the "newdomain.com" location.
To answer your question, will Google see this as duplicate content and penalise you - no - make sure your site has an XML Sitemap, and submitted via your Google Webmaster Tools account.
Leave your old files where they are, leave the old directories where they are, and in time they will disappear and be replaced in the SERPs with the new location. I also... wouldn't delete the old files and directory - just in case you have incoming links from external sites, you don't want to lose that link juice.
Code:
Options +FollowSymLinks
RewriteEngine on
RewriteRule (.*) http://www.newdomain.com/$1 [R=301,L]