If the doctor truly did refuse to give the vaccination, she should have brought in proof. Only a doctors exemption clears you with licensing.
Though, in my experience, California does not visit and check up on providers all that often. If you are newly licensed, you probably could've safely given her a deadline by which to take care of it.
I give parents something like this.
http://www.smmusd.org/CDS/pdf/IMM-230.pdf
I explain that licensing does audit my files to ensure that all children are up to date on immunizations and, if some are missing, my policy is that care will be terminated until immunizations are caught up. As a licensed childcare, I have to stay in compliance. It isn't a choice.
To keep up on when immunizations are due, I review files quarterly and send out a reminder to all parents.