For CRA purposes when doing your taxes, you MUST file as common-law. As soon as the baby was born (and you were living together) tax status needed to change from single to common-law. In this there is no length of time living together required.
Of course for CIC immigration purposes, the only rule is 1 year living together. Having kids is irrelevant to them.
And of course all other provinces then have their own rules for provincial benefits and rights. It can certainly get confusing.