I would start now! 

I started applying for jobs about 6 months before graduating with a BA in Anthropology (Completed 12/2009). It generally takes about 3 months to hear back from the military after applying through USAJOBS. 

Have you thought about graduate school? I wanted to gain paid work experience in the museum field before starting graduate school, but I unfortunately couldn't find a job at the time. I will be done with my MA in Museum Studies this December. I really think the graduate program played a part in landing my new job. I can honestly say everything I'm learning as a graduate student can be applied to my job and vice versa. 

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