Should I use a separate content type?
If you are going to do this often, or expect changes that require these two types to be in sync in the future, you might investigate the http://drupal.org/project/features module, which packages stuff up like this.  But, if it's a one off thing, I'd just go and create a new content type and reuse the existing fields plus the new/different ones in the second content type.  If you don't want to type everything in again, you should be able to use the CCK export feature and then just change the name and type of the result and import it, which if all goes well, will create the second type for you identically to the first.  Then just add the new/different fields manually.