Then you have a problem -- I understand why you think it would be better for your GF to move to be with you but what about her child? If he's seeing the child, then that trumps pretty much everything --
Your GF will have to pick up another job and do what she can to make ends meet. Why don't you supplement her income by sending her extra money? Or is that not possible?
She could give custody of the child to the father and SHE could move.....but I'm supposing that's not an option either. Keep in mind that IF she moved to be with you and the two of you didn't work out, then what happens? She has to start over again?
You could rent out your home and pay someone to help you run your business.....or is that not possible either?