Should I date a friend who's about to graduate?

[Sam]

(TL;DR: My friend, who I may-or-may-not have been friendzoned by, is about to graduate college, and potentially move away. I'm afraid asking her out will make the friendship weird. Also, I'm inexperienced, and don't know how to gauge interest beyond friendship, or ask her out.)

I know this woman who I see once a week at a group we're both a part of. She broke up with her boyfriend a couple months ago. We both go to the same college (I'm 19, she's 21). Unless she finds a good job/internship in our town of 50,000 people (unlikely, with her liberal arts degree & the economy), she'll move back home, out-of-state, in May.

We've known each other for a little under a year, but we're not best friends or anything. I'm wary of the friendzone. I'm also afraid that asking her to a date will make things weird if she says no.

She's had multiple relationships, and I've never even been on a date, nor made it to first base. I can talk to girls and everything, but I don't know how to ask her out, make her know it's a date (especially since we're kinda friends), gauge her interest...

We've been talking to each other more often lately. More one-on-one at the group. A simple Facebook message turned into a 90-minute conversation (where she complimented me by calling me wise). She's taken more of an interest in me on social media. Also, when she said she was bored and had too much free time, she seemed receptive when I offered she should hang with me and my friends sometime.

Do I risk making it awkward, or having a mere three-month relationship? Or do I go for it? If I go for it, how?

(Just curious of feedback. Thanks!)