I hate to nitpick ... wait, no I don't. I love to nitpick. But it's good social graces to claim that you don't ...
The BNA Act didn't 'establish Canadian independence'. It united a few British colonies in North America into one 'super colony'. The new Canadian confederation remained a British colony.
Canada achieved independence not in any one act or by any single action. It slowly evolved over time. (Some would argue that since we still retain the Queen as our head of state that we're still not completely independent. I'm not sure I agree with that, but it's a point worth considering.)
Some steps along that road to independence:
Starting in 1848 the Canadian colonies were granted 'responsible government', meaning that they elected their own local legislative assemblies that could propose and vote on bills but those bills only became law once signed by the governor general which was still appointed by the Queen. (This was in response to the failed rebellions of 1836.)
In 1867 the BNA Act unified the two Canadas and New Brunswick and Nova Scotia. The new confederation meant there were now local provincial governments and a single federal government. Britain delegated responsibility for almost all local issues to these governments. But foreign affairs remained in the hands of Britain.
Over time Canada was given some ability to manage its own affairs with America. But only as long as that didn't go counter to general British policy. And slowly other areas of foreign policy for Canada also transfered to the Canadian federal government. By 1918 Canada has 'independent enough' to be given its own seat at the Paris conference that ended WWI.
In 1931 the Statue of Westminister finally formally transfered all foreign policy (and various other areas that had previously be reserved in Britain) powers for the 'developed colonies'/dominions from Britain to their respective local governments. So this is what gave Canada (and Australia, New Zealand, South Africa, Ireland, and Newfoundland (which later joined Canada)) [almost] full control over it's own fate. This statute is the one most commonly pointed to as 'establishing Canadian independence' if you must point at just one thing.
In 1982 the Canadian constitution was finally 'brought home'. This required an act of the British parliament but after this point Canada was free to modify its own constitution without having to go to Britain and ask for approval. (This is because there was no amending formula prior to 1982.) This is also sometimes pointed to as the point which 'established Canadian Independence'.