That's true, but the US has other checks and balances. Trump, for instance, can't introduce a law or vote on it, not true for our PM.
Realistically, a president can always get a bill introduced into congress by simply calling a friendly congressman or senator. If Trump wanted a bill introduced to name the moon after him just about every Republican would vote in favour, and do so enthusiastically.
I do know that many Quebecers and I assume many indigenous aren't fans of the Crown, which i can understand. It might be unifying to get rid of the Crown, but then the loyalists would be quite upset, so I could see major fights. In this political climate I would avoid dealing with this issue right now.
The loyalists would be more than a little upset, and they'd be furious not just at whatever party was behind it but whatever parties supported it, including Quebecers and indigenous people. And that fury would likely last for the remainder of their lives.
No party is going to do this, though, because there's no political profit in it. There is a tiny group of people who really want to do away with the monarchy, a larger group making up about a third of the population wanting to keep the monarchy, and the rest are 'bleh, whatever'. The bleh people aren't going to reward the party which got rid of the monarchy but the loyalists will despise that party forever.