First your military pay will not be taxable in Georgia, make sure when going through the Georgia State interview that you show as nonresident and your military pay is not counted towards income in Georgia. It should be allocated to "other State".
Also, please be aware that your spouse can choose to have the same state for state taxes as you because of the Military Spouse Residency Relief Act (MSRRA) once you are married. But then her income would be taxable in Michigan and would have to be included on the Michigan tax return. You would have to file a Michigan and Georgia non resident tax return to get a refund on the taxes paid to Georgia.
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