I would probably open up a conversation with her and ask why it's so important to her that you use that specific Barbie. Then, take it from there and explain why you'd like to have a choice and how it may affect you if your choices are taken away. 🙂 There's really not a wrong answer here. It will not necessarily change the course of who she will become if you just say ok I can use this one.
Every opportunity is a teaching moment....definitely would have taught her that everyone has their own opinions or right to choose.....may be a sharing type issue if an only child which is also a teaching moment