Once again, it's a case where it's perhaps unfortunate that words only rarely have precise, unambiguous meanings. Depends what you think "nation" means, or ought to mean. In the context of Quebec the word is loaded with emotional, political, and cultural freight it doesn't have in the context of discussing the so-called First Nations. If you define nation, as one of my dictionaries does, as " a community of people of mainly common descent, history, language, etc., forming a state or inhabiting a territory," then I suppose you'd have to agree that Quebec is a nation. On that basis, so are the Scots, the Irish, the Welsh, the Kurds in Turkey and Iraq, and thousands of other groups around the world. I could probably make a case that Saskatchewan is as well, and we should annex Alberta because such a large fraction of its population came originally from Saskatchewan. History shows that people have used weaker claims than that to justify annexing territory. It wasn't long ago that Iraq tried it on Kuwait.
Then consider the difference between "forming a state" and "inhabiting a territory," The latter is a much weaker condition and I'm inclined to dismiss it because it opens a door to so much potential foolishness. We could have Ukrainian nations in various parts of Manitoba, Saskatchewan, and Alberta, for instance. If you think carefully about what "forming a state" really means, the definition amounts to a tautology: a nation is a group of people who form a nation. Not very useful.
I think the key point has to be sovereignty: no community is a nation unless it has absolute independence and authority over all matters relating to its governance and its relationships with other such communities. So no, Quebec is not a nation. Some people think it should be and are working actively to make it so, but until they succeed (and I'll be very unhappily surprised if they do) the label doesn't apply.