Big/Little Relationship (romantic?)

[mrex23]

Please lay off on the incest jokes because we aren't related at all. We just happened to be paired together as big and little. We get along really well and we generally hang out together alone once a week or so. Sometimes more or less. However, it might be because we are big/little which is why she wants to spend this much time with me.

We got paired up around 2 months ago.
I started liking her after a while and I know it probably isn't the smartest thing, but I did. I really like her because of her personality. It is different than that of my friends. We have conversations that would just go on and on. I always have lots of fun when I'm around her and she makes me smile and laugh. It just feels different being around her compared to some of my best girl friends. We could have conversations about pretty much anything and how we pretty much wouldn't get bored of it. She was even like how she likes how I am capable of carrying a conversation about certain things with her that not even her best male friend could.
I'm hesitant to do anything because she does not like dating within the fraternity because of how quickly things spread and how I guess in a sense "brothers." She will only do it if the guy is pretty awesome, but it also depends on the guy.
Anyways, I really want to ask her out on a date, but how should I do it without it being weird? I want to do it soon because this is both our last year in college. I'm also afraid about the age difference as I am 21 and she's 23. What should I do and say to her? I really like this girl and never really felt I liked someone this much before. How do I go about asking her out on a date smoothly?

tl;dr I like this girl, but she is my big sister in fraternity. I want to ask her out on a date, but how do I do it? We are both last years in college. What do I say and approach situation?