Ku cika wannan magana: "Kwallar Calgary Flames ce ta zabi Quinn a matsayin na 13 a jerin 'yan wasa na shekara ta 2000".
1983 NHL Entry Draft, 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.