Best advice is tread carefully. Leaving aside the very valid point made that it could be in breach of your employer's code of conduct, it could make things very awkward indeed whether things go well or badly. If things go well then it could make things more uncomfortable for your colleagues depending on how workplace interactions change; if things go badly, well, that speaks for itself. That said, I do know of workplace romances which have stood the test of time and avoided the pitfalls, but they are relatively few and far between. By all means get to know her better - in a more general sense, that's part of being a good
co-worker (and probably one aspect I need to improve in my work, but hey) - but anything more than friends is best approached with caution.