Nice to see you again. I'm sorry to hear about what's going on with Nia. I must agree with Kat in that whatever problems you are having with Nia, the last thing you want to do is create a criminal record for her that will stick with her for the rest of her life. I know how angry you must be, but one day she will be an adult woman that hopefully you will be proud of. You're angry now, but a record could affect her schooling, potential jobs, even potential mates.
With that being said, I would consider a few options. One would be to take everything of value out of her room. I know people who have done it, and it's very effective. Wait until she is out of the house and strip her room down to the bare essentials (bed, dresser, blanket, pillow, clothes, shoes), everything else gets packed and put away. When she comes home, explain to her that this is how you felt when you saw your credit card statement....robbed, deceived, lied to. She can do an assortment of services to pay back what she owes, either by doing things around the house, or even better have her do volunteer work at a community center, elder home, hospital, etc. Arrange how many hours she would have to work to pay back the full amount. Once she pays back the full amount, then you can either give her her things back all at once, or you can have her earn those back too. Either box/bag by box/bag, or by the cost of each item.
You could contact your local police department and ask if they have a scared straight program. You could also ask if they could have a cop come to the house and "arrest" her and keep her at the station for a while ( a real arrest might have to be put on record, so they would simply be picking her up, not actually arresting her). You could tell her that you reported the card stolen when you saw the charges and that you didn't know it was her, and that the credit card co sent the police (if the police would agree to do it), I have known police to agree to do things like this for teenagers with problems.
If the police won't do it, perhaps you have a friend who is a lawyer, who could do something similar, pick her up, and take her out and talk to her about the possible charges and where she could end up. It may be less effective, but still helpful, and may work well with a punishment at home.
I see that you mentioned military school. Is this the first time she's done something like this? How does her dad feel about it, have you spoken to him?