The fist thing that you will need to do is to see what the wording of your contract as well as the SOFA with the host nation say. Many contractors to the military are covered under the UCMJ and don't pay income taxes to the host nation while they are overseas and as such are treated as working for the US government. If that's the case, you are not eligible to claim the Foreign Earned Income Exclusion at all regardless of the length of your stay.
If this does not apply to you then you may be able to claim the FEIE. If you are using the physical presence test of 330 days out of a full one year period, the year does not need to coincide with a calendar year. If it doesn't then you must apportion the FEIE between the two years. If you started on 1 July 2012 that would be exactly half for the 2012 tax year (half of $95,100) and half for the 2013 tax year (half of $97,600).
If you later qualify to claim the FEIE for 2012 after filing you can amend your 2012 return to claim it. You can also request an extension of time to file your 2012 return until you do qualify and then file. Since you'd potentially qualify on 30 June 2013 a simple Form 4868 extension request would suffice as it extends your filing deadline to 15 October 2013 for tax year 2012.