Jason, if I read you correctly you are asking if we think you should ask her out. It has been some time since I practiced this kind of thing but from what I have learned,

Do NOT ask her out now.
Think of little ways you can spend time together that are not intimidating.
Do things that involve her saying yes but do not constitute a date like say staying for an afternoon event at school and walking her home.
Working on homework at her house.
Talking on phone and getting comfortable.
meeting her parents so you can see if they are reasonable human beings for her as well as you to deal with. If they know you, then that may be easier to get to going on a date.

When should you try a formal date? A lot depends on things we cannot know.

If anyone tells you to go on the date right away, that is the easiest way to lose a friend.