All you have to do is to go to the CID with a passport copy and ID copy and apply for PCC there. They will ask you for the PCC issued from your country in order to issue you one. You can get your country's PCC once you get the Qatari one.

The PCC of your country must be attested by your embassy and the Ministry of Foreign Affairs in Qatar before going to CID, otherwise, they will not accept it.