The obvious thing is to ask her about her living situation. Could she move in with you. Explain that you have a thing for her and you already are feeling like this kid's dad. You aren't looking for an easy relationship but if she's willing to take a chance and get a bit of relief from some bills, it could work out.

I'd be clear that you in no way want the kid's bio-dad showing up at your place. You aren't against him having a relationship with his kid, but not on your turf, ever!

You will have to be a strong and gentle man to handle this situation. Best of luck bro.