This is not a process you can handle without legal help. You will need to file a motion for removal as well as for an Order permitting the child to travel out of the country. Notice must be sent to your ex and if he does not show up, a court order will solve your problem. If he does show up and contests the removal, you will need good counsel to handle the litigation. You are fortunate that there are many good lawyers in your area. If you do not yet have one, speak to several and hire the one you like best.
Illinois law allows a custodial parent to ask for leave to remove the child from Illinois. This law applies when you move out of the state - whether to another state or another country. The court will look to what are called the "Eckert" factors to determine whether the move is in the best interest of the child. The motivations of each parent, feasibility of a visitation schedule, the effect (or lack thereof) on the child's relationship with the non-custodial parent and the direct and indirect benefits to the child are all relevant.
This is complicated and you should have an attorney help you with this case.