There's no such thing as registering a common-law relationship in Quebec, unless you mean a civil union which is legally entirely different. By common-law partner I mean (as do the federal government statistics I cited) what the Quebec government and legislation often call de facto spouse, de facto partner, or sometimes shoehorn into the definition of spouse despite not being married.
And the taxes aren't always a bad thing. In my case, my partner makes much less income than me, so starting this year we can shift medical expenses to her tax return to save with the medical expenses tax credit. We'll also qualify to share health insurance plans despite not being married.
Let me circle back and invite you to make sure you know all the limitations of being common law partners (which you seem to be). For my wife and I for example, the fear that her parents might have the final say in her health decisions if she's incapacitated meant we needed more than simply common law.
Well, as for that particular point, https://educaloi.qc.ca/en/capsules/incapacity-being-unable-t... makes it appear that spouses and common-law partners and parents are all equally able to submit a request to a court for protective supervision if the person in question hasn't prepared a protection mandate (formerly known as mandate in case of incapacity). And you and your wife were just as able to override that by giving protection mandates to each other before you married as you are now. Do you know otherwise?
In our case, there are strong financial reasons not to get married yet: she's a student receiving Quebec financial aid, and since we're unmarried and childless at the moment, Quebec doesn't consider my income or assets in student aid decisions (unlike how e.g. Ontario treats common-law partners). Once that changes, we may reconsider.
And the taxes aren't always a bad thing. In my case, my partner makes much less income than me, so starting this year we can shift medical expenses to her tax return to save with the medical expenses tax credit. We'll also qualify to share health insurance plans despite not being married.