The deep learning-based ISP models for mobile cameras produce high-quality images comparable to the professional DSLR camera. However, many of them are computationally expensive, which may not be appropriate for mobile environments. Also, the recent mobile cameras adopt non-Bayer CFAs (e.g., Quad Bayer, Nona Bayer, and QxQ Bayer) to improve image quality; however, most deep learning-based ISP models mainly focus on standard Bayer CFA. In this work, we propose PyNET-QxQ based on PyNET, a light-weighted ISP explicitly designed for the QxQ CFA pattern. The number of parameters of PyNET-QxQ is less than 2.5% of PyNET. We also introduce a novel knowledge distillation technique, progressive distillation, to train the compressed network effectively. Finally, experiments with QxQ images (obtained by an actual QxQ camera sensor, under development) demonstrate the outstanding performance of PyNET-QxQ despite significant parameter reductions.