This is the story named in English "The true story of Ah Q." Author Lu Xun transliterates the pronunciation of Q as Quei, and suggests that the Q could stand for 桂, or 贵, which are today pinyin Gui4. I think Lu Xun grew up speaking a Wu dialect, but I am not sure of that. Anyway I am less concerned to know how he pronounced it.
Answers to the question How do Chinese people pronounce Latin characters? suggest it could be pronounced by the name of the Latin letter, kiùr.
How is it said today by Mandarin speakers in China?