I think I would speak to an adoption attorney and find out how expensive it is in your state. It might be cheaper in one or the other.
It can cost $10K or more with legal fees and court costs. I suggest you think about how much you can afford to put towards this.
I also think it's wonderful of you guys to do this. I don't know if you were looking to adopt or not but she must have a lot of faith in you and know you'll love her child.
You do need to think how you're going to address this child's lineage later on. I know some that have open adoptions and the kids grow up knowing they have brothers and sisters and are okay with that. Some that grow up never know their siblings and then in adulthood find out. Those other kids know mom is pregnant and they're going to want to know their sibling. They are going to remember.
My husband's mother was married before to a man and she had a daughter then a son. The daughter she kept and raised. The son she gave to an aunt to raise. It was just found out in the last 10 years that their cousin is actually their brother.
After she divorced the first husband she and the daughter lived on their own for a while then she met my father in law. They married and had my husband. She had another son a couple of years later. She left California one day to drive a couple of days to go visit family. When she got home a couple of weeks later she no longer had the second son, told everyone he died and she buried him. Never, not even when she was going to die, never told anyone where he was buried or where he was pronounced dead.
So the family thinks she gave him away too, but to a stranger some where along her route.
Some people can't handle more than they have.
I am happy you will get to raise this little person. Congratulations.