You know, you're actually at the perfect point in time to ask her out. You two know each other, but you're not at the "absolute friend" stage yet. Ask her to go see a movie, or perhaps for some coffee, or if nothing else just to hang out and play video games. Just spending time with her in a date scenario is a good option.
Whatever you do, do not make the mistake of becoming really good friends with her, because you set yourself up to become a slave to the friend zone. Even though it seems like it makes sense, becoming friends with her so she can see the sweet niceness that is you, it really is detrimental to going out with her, as she will only see you as a friend.
In any case, think about how much you want her, how much you want to be with her, then ask. If she says no, then it wasn't supposed to happen, and she's missing out on a perfect opportunity. And yes, if she says no, it will hurt. It will hurt a lot. But you will get through it. And besides, if she says yes, it will be the best feeling in the world.
But then, why should you trust me? I'm just a random person on the Internet, what would I know of your situation?
To be honest, I know exactly how you feel. I used to be absolutely terrified of rejection, I always set myself up to be friend zoned, and I was always, always, ALWAYS a doormat. What few relationships I had ended within 3 months. It wasn't until college that I started figuring out what I was doing wrong. I learned not to be afraid of asking, to embrace my gut instinct, and, most importantly, to expect rejection. To expect it is probably the best thing you can do for yourself when the time comes to ask. If she says no, you have lost nothing because you figured it would pan out like that. If she says yes, then you will feel ecstatic.
Ah, but I'm rambling. This isn't about me, it's about you. The simplest answer is to just go for it, and it's what I recommend.
Good luck and godspeed.
