Damn... Please update us all with the outcome...
I did literally the same mistake, but I haven't received AOR yet.
We submitted our common law start date as 2021 - 10 - 08 (based on the idea that this is the day we started living together), but from what I am seeing it should have been 2022 - 10 - 08.
How can I fix this now? Is there an online form to update the application or something?
If you have not received AOR yet, you can write now (webform) to correct what you wrote. Just provide tombstone details of applicant and sponsor.
BUT: you do not need to worry quite so much. This idea of the start date of common law being one year from the date of start of cohabitation is confusing and used inconsistently (even by IRCC*). It is very unlikely that they would see this as misrepresentation if all your documentation showed your start of cohabitation as 2021-10, and you should be fine if you have been living together well over a year (eg if you are still living together now).
While it is possible in theory for IRCC to treat any error as misrepresentation, in practice and in law 'honest mistakes', obvious typos, etc., that don't affect anything ('not material') are not misrepresentation.
*There was a case here where IRCC sent a letter saying applicants hadn't lived together for a year because they put - correctly - their one-year anniversary of cohabitation as start of common law, and the officer thought that meant they'd lived together for only a few months. It was sorted out. Basically it would be better if IRCC stopped using this phrase 'common law start date' because every normal human interprets it to mean start of cohabitation.