It was the practice of the Prophet (peace and blessings be upon him):
"He (peace and blessings be upon him) would deliver the sermon every Friday with Surah Qaf."
Hadith Referenceصحیح الجامع الصغیر / حرف الكاف / 4935
Hadith Gradingالألبانی:صحيح
Hadith Takhrij[د] عن بنت الحارث بن النعمان. الإرواء ٦١٥.