In order for you to get a work permit based on being her partner, you have to qualify as her partner. If you had lived together for 12 months or more before she left, you would have been considered a common law husband and had been able to go with her at the time but even if that was the case, now that you have not lived together for the last 2 years, I don't think you could qualify for that anymore. I don't assume she mentioned you either as her common law on her student visa application.
This leaves one option for you to apply as her partner and that is to get married. If you get a tourist visa to visit her, you can get married in Canada. If you don't, she would have to come to you.
If you don't want to get married, you would have to qualify for your own visa to get to Canada, student visa or work permit.
There is no biological father sponsorship available for a girlfriend on a student visa and a minor child. If your child is born in Canada, he can sponsor you when he becomes 18 years old and has enough income to prove that he can support you but that is a long time to wait.
I think you should start by applying for a visit visa to go visit her. If you get married while in Canada, you can apply to extend your visa to match her study visa and you can apply for a work permit based on her visa as well.