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They'll only come after you in the U.S. if you owe money in Canada. If you have an order that expires when your child turns 18, then there's no reason for anyone to come after you in the United States after you stop paying, as long as there aren't past due amounts. The state of Illinois shouldn't even know that you have a Canadian child support order unless it's been registered with the court where you live (which typically would only happen if you missed payments).
The age at which child support terminates is based on where the court order was entered. You may want to verify with a Canadian attorney that your obligation to pay support DOES terminate automatically on your daughter's birthday and that you don't have to do anything to make support end, but the U.S. won't take any interest unless the custodial parent tries to collect money from you in the U.S. If you are supposed to file for termination and you don't, you could wind up having to pay more just for not following procedure, and you don't want that.