If the two websites should be identical but available at separate domains and you use relative URLs throughout your site this is actually quite simple. This is assuming you want all links available at both domains.
Direct the new domain name to point your Drupal install.
Depending on your system configuration there are several ways you may need to do this. If you have a dedicated IP you can simply point your domain to the appropriate IP and ff you use virtual hosts you may need to setup a symbolic link.
ln -s /var/www/example.com /var/www/newdomain.com
All relative URLs should inherit the currently loaded domain name.
I believe for this to work though you will need to leave $base_url commented out in settings.php.
* Base URL (optional).
* If you are experiencing issues with different site domains,
* uncomment the Base URL statement below (remove the leading hash sign)
* and fill in the URL to your Drupal installation.
* You might also want to force users to use a given domain.
* See the .htaccess file for more information.
* $base_url = 'http://www.example.com';
* $base_url = 'http://www.example.com:8888';
* $base_url = 'http://www.example.com/drupal';
* $base_url = 'https://www.example.com:8888/drupal';
* It is not allowed to have a trailing slash; Drupal will add it
* for you.
# $base_url = 'http://www.example.com'; // NO trailing slash!
Using this method I rarely have to make custom edits. This includes views output. Just make sure you always use relative URLs.
If you want the content split up between the sites or want to make change the theme or layout you may need to do something a bit more complex.
There are other more robust and complicated ways to separate out your content. A few modules and concepts that come to mind include...
- Domain Access
- Multi-Site (Added for reference, does not meet your requirements.)
- Virtual Sites (Disclosure: I haven't used this.)
- Duplicate your sites (As you mentioned in your question)
I will try to update my answer to be more appropriate with your feedback. Feel free to add details about your hosting environment and how and if the content will be split.