"quality of which" is a perfectly correct and usable phrase in written English.
You can use it to refer to a previously-stated noun. For example: "The coffee was fresh, the quality of which I greatly appreciated."
They seep into surface water, the quality of which is also below EU guidelines.
There can be few paintings of comparable quality of which less is known for sure than The Polish Rider.
That patty is made of ground top sirloin and shoulder, the quality of which seemed to be top-notch.
The band are on the cusp of releasing a new album, the quality of which is difficult to judge tonight but sounds the same as the last one.
The school also makes its own compost, the quality of which much impressed Prince Charles when he paid a visit last year.
A third key component is a significant increase in the number of coach education programmes, the quality of which, Berger states, is "comparable to those in Europe".
Like a good sense of humour or the ability to carry a tune, compassion is a quality of which we all suspect ourselves.
The next day he returned and watched two hours of character dancing, the quality of which impressed him more than the exhibition of classical steps.
The value is in the execution, the quality of which is made more obvious by the nature of the topic: love — or bad-love — songs.
Yet from time to time he played an innings the dash and quality of which – even if India ended up losing – no onlooker would forget.
The offerings, the quality of which proved surprisingly high, were then pushed out to another twenty workers who voted on which was best.
