Training her now in a crate is a good idea and then talk to the vet see what he can give her to keep her calm for the trip. I now how hard it is, the thought of a loved one in the baggage compartment of a plane. I had to do that twice in my life time and it about killed me. I worried the whole trip but it all worked out fine. I'm sure it will for you too.

There really not much other advice I can give you, inless you want to pay someone to drive her to Chicago.

BTW: Enjoy Chicago, my brother lives there and it's a great city. As long as they don't get those -20 degress days, like the one winter I was there.