If it is your desire to maintain contact with your child, share custody, and insure your rights as to the child are maintained, you need to see an attorney immediately. You should understand that you will probably be required to pay child support until the child reaches adulthood. Also, since you are not married, her rights to determine where she resides with the child may be greater than if you were married. Such child custody issues must be handled through an attorney in order to assure your rights are maintained.
In Illinois you have certain protective rights to the visitation and physical possession of your children. As a father though the laws that ensure your rights only come into play after it has been legally established that you are the father. This is not accomplished by your name being placed on the birth certificate. It is accomplished by you signing a voluntary acknowledgement of paternity or having a determination of parentage through the court system.
In the event you have already been legally declared the father I suggest you file a court action pursuant to the Illinois Parentage Act, 750 ILCS 45 to prevent her from taking the child until the court can make a determination if this move should be allowed. It may be a good idea to get an attorney if at the very least to ensure you get your case into court quickly.
One of the first steps would be to make sure you are legally recognized as the father of the child. Please make sure to see an attorney as soon as possible. Time is of essence!