As far as I'm aware, Canada and my country, Australia, have broadly similar histories regarding their key allies in the twentieth century. Both started the century as dominions of Britain, and contributed to Britain's military endeavours early in the century. By the end, both were dependent on the US as their chief military ally. In Australia, we tend to date the transition very precisely: World War Two, particularly the Fall of Singapore, when it became apparent that we couldn't rely on Britain to protect us from Japan. My question is whether Canada has a similar event which marks their transition?
So I would trace the origins of defence coordination between Canada and the United States to approximately the Second World War as well, although unlike Australia there was not necessarily one "defining moment" that made this shift attractive.
As early as the 1930s, the US had been pushing for greater defence accommodations with Canada, an impulse that Canada largely tried to resist. FDR proposed building a military highway to Alaska, something that prime minister William Lyon Mackenzie King shot down. Meanwhile, officers within the Canadian military urged King and his cabinet to increase military spending to allow for rearmament, hoping that this would discourage further US attempts to extend its military presence into Canada. During this era American generals had very bellicose ideas regarding Canada, and went as far as to consider the ability to reach Canadian cities in the event of an American invasion when selecting places to build military bases. King fought very hard to keep Canada within Britain's sphere of influence when it came to defence.
When Canada entered the Second World War in 1939, the needs of wartime made cooperation on continental defence more attractive. In 1940 King and FDR met in Ogdensburg, NY to discuss what would become the basis of Canada-US defence relations. The Ogdensburg Agreement established the Permanent Joint Board on Defence (PJBD), a forum staffed my military and civilian representatives from both countries and recommended areas of cooperation. One of the largest considerations was that both Canada and the US were providing significant amounts of military equipment to Britain, although the US was not a belligerent at this point. Ogdensburg was followed in 1941 by the Hyde Park Declaration, which harmonized production of war materials and included Canadian-produced materials destined for Britain within the existing Lend-Lease Agreement. As a result, tariffs on military goods of this nature were waived when crossing the border. Although the impetus behind these agreements was to allow Canada and the US to cooperate to support the Allied war effort, they were also a recognition that both countries had a shared responsibility for the defence of North America.
After the war, areas of cooperation between Canada and the US deepened. In 1949 Canada and the US became founding members of the North Atlantic Treaty Organization (NATO), which tied Canada and the US to western European countries in a mutual defence pact. Also included in NATO, which remains a cornerstone of Canadian defence policy, were provisions for greater harmonization of tactics, equipment, etc. across member nations. The modern Canadian military has a large degree of inter-operability with the US, even if the underlying traditions and structure of the Canadian Armed Forces (CAF) remain British in origin. The final significant step towards continental integration was the creation of North American Aerospace Defence Command (NORAD) in 1958, a joint-venture between Canada and the US to monitor North American airspace for potential threats. Although born out of Cold War fears of Soviet aggression, especially considering that Canada was on the flight-path of potential Soviet attacks on the US, NORAD still operates today and allows for significant intelligence sharing between both countries. During 9/11, NORAD scrambled fighters from the US and Canada to patrol North American airspace for other similar threats. NORAD was renewed, permanently, in 2006.
I hope that I have (mostly) answered your question!
TL;DR: The needs of the Second World War, and then the Cold War gradually pushed Canada towards embracing military cooperation with the US, an impulse that Canadian governments had resisted as late as the 1930s.
Further Reading:
John R. English, “Canadian-American Relations,” The Canadian Encyclopedia (September 2009)
Azzi, Stephen. Reconcilable Differences: A History of Canada-US Relations. Don Mills: Oxford University Press, 2015.
Perras, Galen. “The Myth of ‘Obsequious Rex’: Mackenzie King, Franklin D. Roosevelt, and Canada-US Security” in Transnationalism: Canada-United States History into the 21st Century edited by Michael D. Behiels and Reginald C. Stuart. Montreal: McGill-Queen’s University Press, 2010: 203-223.