I am answering this Question with a basis in California law. If there are no court orders at all in place regarding custody, there is nothing to dictate that one parent has greater custodial rights then the other. Therefore, if you are the father, have the child with you, there is no court order telling you otherwise, it would not be a violation of any law to move to the next county. On the other hand, if there are formal orders in place, you would need to read the language of the order to see if there are any restrictions on moving.
If there are no court orders in place limiting where you can live with the child, then no, you could move. However, I do advice you going and getting a paternity case filed and ruled upon to limit problems in the future. Now seems like a great time based on your facts to file as you should easily be given dole managing conservator rights and duties, which would prevent mom from coiming back to bother you when she gets out of the pen.