Advice on a girl - having trouble with what I should do

There is this girl that shows interest in me. We hang out almost every day and she's usually the one to call me. I show her that I like her, and has a clue about how I feel and I think we would make a great couple. The thing is, some days she gets into depressions when she is reminded of her ex boyfriend. I've been in relationships before where there were remaining feelings from a past relationship and it was more trouble than its worth. She has made obvious hints as to how she's alone and tired of being alone and needs a boyfriend, but would I just be replacing her ex? I'm at a point where I want a serious relationship and I feel that if this is to work out that she needs to start fresh and without any prior attachments...I don't want to be a comparison to the ex. On the other hand, I'm afraid that if I don't act soon, I'll loose the chance completely, but it's hard to tell. Plus I'm tired of being alone myself and we would be able to keep each other really good company. Any advice or wisdom on this would really help me out as I'm just really confused about the whole situation.