Guardianship is a pretty extraordinary remedy, especiallly where the birth parents are still alive. You would file a petition with the assent of the mother. However, you will also be required to give notice to the father, and ultimately a hearing will be conducted in which all parties will have the opportunity to present their point of view. It is likely that the court will appoint a "guardian ad litem", who will investigate all of the facts and circumstances in the girl's life, and then make a reccomendation to the court as to what is in the best interest of the child.
The next complication is that if the father is now enlisted in active duty in the military, under the Servicemembers' Civil Relief Act (SCRA) he may be entitled to a stay of any proceedings until such time as his assignments will allow him to participate.
I highly reccomend that you get a consultation with an experienced probate attorney in the area where the girl lives.
This answer is provided for informational purposes only. Actual legal advice can only be provided in an office consultation by an attorney licensed in your jurisdiction, with experience in the area of law in which your concern lies.