J.C.
I grew up an only daughter of a single-father after mom left when I was very young, so my perspective is a little different than some. And my dad and I moved a lot. He was still trying to find himself. He was mostly a fabulous father, but still lots of moving.
I think you need to think long and hard about what really is best for her and not what you need. If her dad is in a stable healthy relationship now, and there's stability in the household with siblings to love, close family nearby that's worth a lot. And if he or step-mom don't work full time so can spend more time with her. Of all the military kids I know they all wish they'd been able to stay in one place more, especially when they get to school age.
You might also try some counselling with her to see if there are issues you could resolve that would make things better for her with you. And put the agreement in writing and under what terms it can be changed again.