Luckily for you, I had to go through this during the summer, so I have a little bit of perspective.  As the other guys are saying here, steer clear if you can.
1.) You hint that she's in your department. That means you'll be seeing her for hours on end EVERYDAY. At my internship, I was seeing this girl about 80 hours a week. Yes, it was a lot.
2.) If any of your co-workers can tell you're hitting on her, that's trouble. In my case, I apparently make it obvious to onlooking girls if I'm hitting on someone, which would explain why my boss was laughing the first day. Soon after, the other people in my department were joking with me about it. I wasn't too happy about this.
3.) People talk. Rumors fly. I'm not sure you want this topic to be the focus of half the conversations you'll be in.
4.) It could take away from your work and hurt your image. Luckily for me, I was able to separate my actual work from this, but it's a dangerous line. You don't want the first thing people know about you being, "he's the guy trying to get with his co-worker."
5.) It forces you to act more cautiously than normal, not helping your game. If you get rejected, then the office environment is going to be awkward. It's worse if others learn about it too.
6.) Finally, she'll likely sense it immediately. Now I got the girl who wanted to play games with me, I was off-the-mark until the last day when I finally hinted that I'm not dealing with her bs anymore. The night before, she acted in a disrespectful manner and I don't handle disrespect well. I didn't flip, but she noticed that I barely talked to her for half the day (our department boss wanted everyone to be nice during the final afternoon).
In short, I wouldn't do it. It'll give you a lot more trouble than you think.
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