Kokanee speaks the truth and you can fly with it easy.
However if you are already flying with a number of bags and parcels, checking the gun case as extra luggage at the Airport might cost as much as shipping it. So shipping it might save a small hassle, time and money in the Airport.
One thing to be aware of if you ship it would be your potential lack of identification. I doubt you will have a new drivers license yet. If delivery fails for some reason (ie driver is lazy and doesn't want to make the attempt) and is held at the post office for pick up, if you don't have proper ID or proof of address for your new location they may not release the package to you at all. If you can mail it to a friend or family member who already lives there it might be better option if you go the shipping route.
Just my obsolete two cents.