My daughter had a room that was even smaller (and no cupboard) when we downsized. She had a day bed, which allowed for extra storage, but the saviour was an armoire due to height storage vs a dresser taking up floor space.

Placing a day bed on the outside wall may allow for both side walls to be used to their potential. If she wants to have a friend sleep over, you give up the storage drawers for a trundle.

You could somehow seal the door or place a night stand in front. I wouldn’t feel comfortable with a third floor balcony.

An armoire on one side (use baskets to separate the types of clothing). You could look for a second hand piece and chalk paint it a great color.

On opposite wall, add a desk/vanity with lots of drawers and shelving.

IMO you can't block that balcony door since that is the only other egress from that space . But maybe the door can have the swing reversed. That leaves the side walls for a bed so a twin with storage under it and a really good organizing of that closet for clothes that need to be in there all the rest in the storage drawers. I think if renovating is in the future that balcony could sure be more useable as bedroom , shame on the architect that designed this upper floor. IMO the smallest bedroom really is 10x10 . Maybe some shelves along the left wall for some decor too. I think you will need to trust her to be careful and make the balcony a cute place for her to sit and read or play , at 9 she should have good sense and the fact she is a girl instead of a gutsy boy is a bonus.