Is there anything I need to do or know before I can move out of state with my special needs child?

You need to give written notice so the father has a chance to object. Your husband is the child's legal father since you both perpetrated a fraud by putting his name on the birth certificate. If he signed the affidavit of paternity less than four years ago, he can go back and deny paternity. I think you need to address the issue of how you are going to support yourself especially if he is within the 4 year frame for denial. If he objects and makes a motion to the court, you will have to explain your reason for moving. In the absence of a job, there doesn't seem to be much of a reason.