My child is 3 months. Old. The father is not on the birth certificate and does not have court ordered visitation or custody. He hasn't even acknowledged any sort of paternity. I want to move to a different state. I currently live in Wisconsin and he lives in Illinois. He does not pay any support, he has told me numerous times that he does not want any sort of custody of the child, and that he wants her to remain with me.
Can I legally just pick up and leave, or do I need to do something?

No

Actually yes you can. If he has not went to court and proved that he is the father, and if he has not got any court ordered custody. Then there is no legal document to stop you from moving.

Also the fact he is already in another state, since normally the rule included in many custody agreements do this to stop the one parent from moving away from the other parent.

Now you do need to file for child support, at least after you move. It does not matter if he wants to visit the child, or have anything to do with the child, This is money your CHILD is suppose to be getting for the benefit of the child