بسم الله الرحمن الرحيم،
Assalam alaikoum dear brother,
First, I think it's important for you to find out if marriage is something that's on her mind right now and if she is open to meeting a potential spouse. A way to find this out is through mutual friends or maybe even her brother. Try to find out where she stands in life, where she sees herself in the near future and what her view on marriage is (and if it's possible: find out what she thinks of you).
Secondly, before you make this very important decision, I think you should ask yourself if she is worth risking your friendship (of masha Allah 9 years) for. If you truely believe she is, you can take more serious steps...
I would not go behind her brothers back, I would first tell him and ask him how he feels about it. Tell him that you respect him and his family and that his opinion matters to you. If he's okay with it, he could be the one that informs with his sister. If he's not, than you haven't lost the friendship with the whole family... and most likely not even with her brother. Because you handled it in a respectfull way.
Ofcourse it also depends on your relation with her brother... and in the end you are the only one who can judge the situation the best.
Lastly, I advise you to pray salaat al istikhara. No matter what you choose to do, ask Allah for guidance and ease. And hopefully things will work out for you.
The best of luck,
Wa salam
Edit: I'd like to add one thing to my previous post: I'm in no way, shape or form encouraging you to pursue her in a non islamic way. That's why I think you should get one of her mahareem involved: in his case her brother.