I have a dear childhood friend who was nine years older than her youngest sister and who ended up doing all the work that a nursemaid, had one been available in the 1950s would have done. I also had a less close friend who was the eldest of a family of 22, Both of these girls would readily have jumped at the chance of getting away from being their younger siblings' nursemaid. So I understand your GDs request and your willingness to have her live with you.
In the west of Scotland when I was growing up, the eldest grandchild frequently lived with a grandmother and it didn't seem to affect their relationship either to their parents or siblings.
As the others say, give it a trial period, if her parents consent - without that you can't do anything until she is 16 as far as I know.
She is old enough to want to be an adult, if treated like one, so have a frank talk with her about chores, when she has to be home at night, going out with boys!, smoking - it's an endless list, and remember too that however grown up she feels she is, half the time she is still a little girl, taking her teddy to bed. (And long may that last). If she moves in with you, a frank talk about sex is indicated too. They don't know everything at that age, even although they say they do. (Said the retired school mistress!)