Here is what I did:
I hired an agent (Helpline Group) to do this for me since I was not in Qatar anymore. They told me that as per policy, CID doesn't issue police clearance certificate for the period spent on visit visas in Qatar but only for the period covered under work visa/RP. So I got the PCC issued for my work visa period, attached the same with my application, explained the situation in the letter of explanation and also attached the emails from agent. Everything went just fine and my application was approved.
Good luck to you.