Qatar's situation is not much different than UAE, small country with small local population with no appetite for war or conflict but massive natural resources and rich nation, but given Qatar now has militaries from many countries, like America, Turkey (was planning i think?), French, so adding Pakistan will be complicated, now unless in coming days if America reduce its presence in Middle east which i don't see it happening, this might be a bit complicated thing. Plus Pakistan promising forces, Sq of fighter jets to a country without making sure that our own strength doesn't lack behind is also a concern, if reports are true than we already send 18 fighters to KSA without replacing them in Pakistan, we are already short of Sq compared to India, and if we send 1-2 sq for KSA/Qatar we will compromise our own security given the hostile nature of Galeez qoum next to us.
Now unless the new J-10CE's numbers are increased to 60-80, and we get 1-2 more JF-17's sqs I don't see much coming out of this Qatar joining the PACT, or maybe it will take couple of years before Pakistan is in position to spare jets, AD systems and troops for Qatar.