To be fair, Canada's not _actually_ independent yet. The queen is still our head of state, but that probably lasts only until she actually tries to act like it.
She's the head of state, not the head of government. She doesn't have the power even theoretically to make any executive or legislative decisions. Aside from "representing" Canada in a very vague sense, the closest thing to real power that she or her representative (the governor general) has is to "decide" which party to ask to attempt to form a government after an election. This is basically always simply the part with the most seats, barring very rare exceptions.
Anyhow, tl; dr: Canada is most certainly independent, and gained its independence peacefully (although there were minor conflicts prior to that).
He said she was the head of state. I don't know how this disproves the point that the queen has no legislative or executive powers in the Canadian government
The Sovereign may recall the Governor General, or request that their Governor General dissolve Parliament and call an election and the Governor General is compelled to comply.
Ultimately, all legislation requires Royal Assent, and all executive powers are granted by the authority of the Sovereign, who may revoke them at their will and so force an election.
I still sort of liked it when a couple of French colleagues, who had moved to Francophone Quebec, eventually applied for citizenship, and took the oath... to Queen Elizabeth II.
Canada is a completely independent and sovereign state. The fact that the Queen of Canada and the Queen of the United Kingdom are the same person is incidental.
Would you say UK is not _actually_ independent because it's a constitutional monarchy? If not so, why would Canada be any different?
Read the page you just sent me. I challenge you to find any mention of any country other than Canada.
Yes, Canada is a monarchy, yes, the Queen has the ultimate power in theory, but the head of state is the Queen of Canada, not the Queen of the UK.
I'll repeat myself, them being both the same person is incidental, if you think the fact Canada being a monarchy means it's not independent, does that also mean the UK is not?
I think you're being overly reductive. The Queen of Canada and the Queen of the UK, being the same person who wields Sovereign authority over both, cannot be independent of herself.
Anyhow, tl; dr: Canada is most certainly independent, and gained its independence peacefully (although there were minor conflicts prior to that).