Kammala jumla mai zuwa: Wanda Kingston Frontenacs ya tsara a zagaye na farko (na biyu gabaɗaya) na Zaɓin fifiko na 2009 na Ontario Hockey League (OHL), Quine ya buga wasanni 252 a OHL tare da Kingston Frontenacs, Peterborough Petes, da Belleville Bulls, yana yin rajistar kwallaye 90 da taimako 128 don maki 218, da kuma mintuna 218 na hukunci. Bayan kakar 2010-11 OHL, Detroit Red Wings ne suka zaba Quine a zagaye na 3 na 2011 NHL Entry Draft duk da haka, bai sanya hannu tare da Red Wings ba kuma ya ci gaba da buga wasan hockey na matasa a OHL. Bayan kakar OHL ta 2012/13, Quine ya sake jin sunansa a cikin
NHL Entry Draft, wannan lokacin da New York Islanders suka zaba shi a zagaye na 6.