Rubuta ci gaba don wannan sakin layi - Quinn an tsara shi a 13th gaba ɗaya ta Calgary Flames a cikin NHL Entry Draft 1983
, yayin da yake wasa da Belleville Bulls na Ontario Hockey League (OHL). Quinn ya fara zama tare da Calgary a tsakiyar kakar wasa ta gaba, inda ya zira kwallaye 52 a wasanni 54. Lokacin da aka kira shi ya kasance yana jagorantar OHL a cikin maki tare da maki 59.