Hello Arya,
I dont think there is direct integration between PS and QM. But yes there are certain points which should not be ignored like you need to check the QM is activated for movement types. Also, 01 and 05 inspection types for incoming and finished inspection points should be activated as well and attach your WBS to each inspection lot.
So I feel that you need to focus more on movement and inspection types.
You may also execute transaction OMJJ and look for origin type which is assigned against each inspection type/movement type in customization. Now, maintain this inspection type in material master so that during posting, inspection lot will be created.
Regards,
Amit