In this case, I would suggest that write an email to your visa office (using the same email thread in which they requested to send the PCC) that you're here in UAE only for the last 5 months only.
I too had received email in which they asked to send PCC from Pakistan, but since I've never lived there - I wrote an email to them informing that I've never lived in Pakistan and they cancelled that request and just accepted the UAE PCC.
At the same time, also visit the GHQ and tell them that you require the PCC, in case if they are ready to issue.
But yes, you'll need to arrange and hurry up for Pakistan PCC