It should not be.  The default Web site is like any other site and can have multiple Host Headers as long as all of them are intended for the same Web site or application.  Now, if you have some other site running from that Web site (maybe Sharepoint) you should create a new Web site (preferably) or a new Virtual directory for DNN.  You don't need to reinstall DNN for any of these changes by the way.  If you create a new Web site, just use the physical directory for the DNN directory.

CORRECTION:
Just realized that I emphasized the Default Web site and did not consider you already had a Virtual dir.  In that case, all you are missing is the Portal Alias.  It should be specified with like "mydomain.com/dotnetnuke" minus quotes.  If it does not work right away reset the application.

Carlos