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chakrab said:
actually i wasn't mentioning if or who can claim benefit, but the fact that the OP has to claim himself as common-law as his status to the CRA. so it's odd that his marital status is different in different govt institutions.

I agree. Even Alberta government doesn't recognize common-law until 3 years has passed. That doesn't stop them from claiming federal benefits but wont be able to claim Alberta provincial benefits until they meet the 3 year requirement.
 
Andrei13 said:
It is sad that having a baby here, it takes so much time for someone to obtain the working permit. In our case, if my girlfriend will have to leave the country because her status expires, I will definitely have to let her take our daughter as she is the mom and she can raise her better. This will make our life so miserable...

She should not have to leave the country. Just get married immediately and submit an INLAND PR application. She will be at least under implied visitor status during the entire processing time to stay in Canada, and will be eligible for an OWP after stage 1 processing is done (around 10 months time).
She will just not be able to work during the time after her current working holiday visa expires, and before she is eligible for OWP.