I consulted a lawyer on the part about freedom of movement and establishment, meaning the right to move from one province to another. He didn't give me a legal opinion, but he did give me a written answer.
He didn't feel that this violated a citizen's freedom of going from one province to another because if someone passed their citizenship test in Ontario, they could come to Quebec. At the same time, if someone passed their citizenship test in Quebec, they could very well settle in Ontario or elsewhere.
So this doesn't violate that section of the Constitution.