Split a room, is it fair?

I am 13 and my little sister is 9. We have shared a room as long as I can remember, and now that I am getting older I realized I want a room to myself, to have a private place that I can be in without my little sister always barging into the room because it is 'her room too'. So, we have a very large gameroom. It was supposed to be a garage when the builders were making our house, but my parents decided to move our garage to a different place. It's well over 20x25 feet in size. Practically ALL of my sister stuff is in the gameroom except for her bed and a couple of random items. (we have a bunk bed) I asked my mom if she could just make the gameroom her official room, but she said no because it is "Everybodies" room because our Wii is in there and supposedly when our friends come over they all have to sleep in there, even when we normally sleep in the living room. But anyways, I have a new idea. If I could turn half, or even a third, of the gameroom into her room, there would still be a very large area left in the gameroom, AND I could move my little sister in there. We could divide it by curtains, which are very inexpensive, and which I would pay for. I would give her the whole bunk bed and the dresser, and the nightstand, for her new 'room'. (Because, after all, they are all flowery and girly which I liked when I was 5 but now loathe) I'd just have the matress and bedding. I would be fine with the matress and bedding, and there is also a bookshelf and desk with my computer on it in my room. (my sister has her own computer in the gameroom, and multiple shelves with her toys) Is this fair? I am going to tell my mom and sister about this, and how it will be free for them becuase I will pay for everything, but I wanted some advice on this first. It sounds pretty fair to me, but what do you guys think?