You probably want to speak to your host about this. They can usually offer some insight. You might be able to just add an addon domain in cPanel. However, you will have to also change all references of the old url in your database (see the plugin I mention at the end of this post).
If you’re moving to a totally different url, then it would probably be best to move your site:http://codex.wordpress.org/Moving_WordPress
Essentially, you need to:
-Download your entire WordPress directory with all plugins, themes, uploads, etc
-Export your database via phpMyAdmin
-upload the file to the new location
-import your new database
You will probably have to make some changes in your database (ie change all mentions of old domain to new domain). This plugin will help you make those changes in your database: http://wordpress.org/extend/plugins/search-and-replace/