The bible, as far as I remember, doesn’t speak much on the topic, as it wasn’t a huge/common discussion or concept in biblical times. However, in the world we live in, I’d say it’s okay, especially if you really believe in your convictions to do it, and hope to do good there. Varying people might feel differently about the military in general, and will tell you differently, but God is generally fond of people who chase what they feel called to do.
I think that women being in the military is 100% okay! My priest was a chaplain and when he came to my school to give a presentation he asked if anyone in our high school was planning on going into the military. Only one girl came forward and my priest had no problem with it at all. 🙂