I guess a simple solution is to edit the email template and add a tracking link:
http://nolp.dhl.de/nextt-online-public/set_identcodes.do?lang=de&zip=[ZIP]&idc=[TRACKINGNUMBER]
You only need to use the DHL extension if you're going to ship through DHL and you want to use their live ship price calculator. Otherwise, you only need to go to System -> Configuration -> Shipping Methods -> DHL, and fill in the necessary information. You'll need to get the Access ID, Password, and Account Number from DHL. The rest are personal preferences.
Best Answer
You need to go to the DHL website and register an account in order to receive an Access ID, Password and Account Number:
http://www.dhl-usa.com/en/express/shipping/open_account.html