So, you have been together for a while. Everything is going well, except for one thing, you want kids and your partner does not. It is not very typical, is it, for a woman not to want kids. However, there may be many reasons why it is so.
First of all, the timing may not be right. Perhaps it is too early and she is not ready. Or, it is too late and you did not really listen when she wanted to have kids and you did not.
Wanting different things in a relationship is a huge problem. And you should know that. Especially when it comes to having children. Counselling would probably be the best option if you want to somehow resolve your problem. And communication is definitely the best solution. You need to talk about this and decide where you want to go. Also, you need to know why it is that your partner does not want to have kids. Once you know the cause it will be much easier to deal with the problem.
However, if you think that you cannot find a solution, the best thing to do is to leave and look for a person who will be a better match for yourself. If there are things you do not really want to miss out on, then do not miss out on them simply because you have a partner that you do not really want to break up with.