I know of no reason as to why in your current situation you should not be able to move immediately (assuming that there are no Illinois court matters now pending which need to be resolved first).
If you have any type of court order regarding his visitation or you staying in Illinois that would guide your actions and you would need to go back into court to resolve it (which given what you posted, you should be able to do). You should speak with a family law attorney.
You do need to consult a family law attorney -- was there ever an order of paternity and/or a visitation.custody order?
You may need to get the courts permission to move out of state -- which would not be a hard thing to do. Further, even though the father is in prison that does not relieve the obligation to provide child support. Whether he may or may not get visitation depends on what he is in prison for -- there are certain statutory crimes in Illinois that a person cannot get visitation if they have committed and been convicted of those crimes.
Consult an experienced Family law attorney in yoru area -- if you do not know of one the Illinois Bar Association operates a lawyers referral service called IllinoisLawyersFinder. Call them and the attornies on that list will privide a 1/2 hour consultation for no more than $25. You certainly need to know your rights and protect your daughter's rights.
If the person you believe to be the father has been declared by the court to be the father you are required to file a petition to remove the child from the state. Please see the Illinois Parentage Act, 750 ILCS 45
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