Dude, if I were you, I'd get away from that situation... the girlfriend and her mother. It doesn't seem to me - from what you write - that this girl cares the least bit about you. You'd think if you two were in a good relationship together, and wanted to make things work, she'd WANT to be living with you, as a family.
As for how much money she'd get, common-law or single... it doesn't matter! Why is she even THINKING of how much money she could get out of you, unless she doesn't want you to be a part of HER life, and simply expects you to pay child support - which is what it sounds like to me.
Like I said, I'd get away from that situation. It's unhealthy for you, and for the baby. A child should not be raised in such a tense situation.
If I were in your shoes (and male)... I'd do the following:
1. Verify paternity of the child (even if you're 100% sure it's yours).
2. Find a place to live that you can AFFORD (even stay with your parents for a while) and close to your work.
3. Confirm your marital status - common law or single?
4. File for custody/access ASAP, and file a child support order based on your 2007 tax assessment (line 150) amount and begin paying.
5. Try to arrange a fair visitation schedule. The norm is one midweek visit, and every-other-weekend Friday-Sunday. However, with how young your little guy is, I'd suggest one midweek visit of a couple of hours, and one weekend day-visit, 12pm-6pm, until he's a little bit older when you could begin taking him overnight (Friday-Saturday or Saturday-Sunday) each weekend.
Either way, start protecting your rights. It seems that this "girlfriend" is simply thinking about the money she could get out of you. You be the parent, and think of your son.
(My fiance was in a similar situation as yours - one night stand gone awry, then having to learn how to protect his rights and be a parent from the moment his son was born and it was clear that he was the father. So if you have any other questions, etc., feel free to message me.)