That is her birth certificate. It will suffice for any request for a birth certificate. She is a US citizen. She can get a passport, SSN, etc.
OHHHHH. I misunderstood. You want a copy of her birth certificate. I don't know. Contact the branch of the military her father was in, I assume the army, or maybe just some office at the DoDD. They should be able to direct you to the proper office.
Good luck.