Qatar operates latest F-15 variant, Eurofighter typhoon, Rafale and Mirage. The chance for Qatar buying JF-17 is slim. Why would Saudi Arabia block the deal and why would Pakistan listen to Saudi Arabia when conducting business? Qatar is like the size of Al-Khobar city if not smaller. If things go south, Qatar will get spanked without military involvement.
Qatar bought these not because they can operate them optimally, but as protection money to the West. Pakistan too can play the same game, sell JF-17s as a package - with weapons, fighter pilots, training, maintenance. That is something the West is unable to offer.