Re: What's the best thing to do?
If you really do want her back, I suggest you move faster than not. A long time ago, I was the one in your ex's shoes. My girlfriend of two years broke it off with me bacause we were just going through a slow phase. She came to me a few days later and told me she thought she'd made a mistake. I told her I was really sorry to hear that but she broke my heart and I was ready to move on. Turns out that at that moment in time, I just could not forgive her for hurting me like that. I hope that if you really do want her back, she doesn't feel like I did way back then.
Also, in your case, I'd look very deeply into the reasons why you thought breaking up was the way to go. Is it possible your instincts are better than you think? I don't know the answer but I will say that if you were with this girl for a year and a half, you don't "get over" that in a couple days regardless of who made the move to end things. It could easily take a few months! Please proceed carefully and I wish you all the best!