Find a local dealer to you that will accept transfers from out of state. It also may be cheaper for your daughter to send the gun from an FFL in her state, since dealers can still send by USPS, while sending a handgun via courier such as Fedex and UPS is getting complicated and expensive for individuals.
EDIT to add: Check your local laws since there may be some restrictions especially if you live in Chicago. handgunlaw.us is a good resource.