You also need to make sure your Ohio license is still valid. Some states require you to notify the DMV within 30 days of a permanent move, and some immediately cancel a license when you move abroad or out of state. (Virginia is one such state - they require you to notify, and invalidate you license when you move out of the state; the license is also invalidated if you do not inform them, and cannot prove that you reside at the address on your license.)
Some states don't care, but in case of an accident, you don't want to find that you were driving without a valid license. The expiry date may not mean anything depending on Ohio law.