As above, you can potentially work through issues relating to marriage, depending on what they are. You can also work through issues relating to living together, particularly if one person just isn't ready for it yet. Whether or not you want to have children is different, though. People do absolutely change their view on that over time, and whereas someone in their early or mid 20s may simply not be able to comprehend the idea of having children, even a few years later that mindset can be very different. Like everything, the key is to communicate to establish whether or not the difference in that respect is likely to be something that changes over time or not. If it isn't, there is simply no way around the fact that one of you wants children and one doesn't. It's an absolute deal breaker.
In this situation it's telling to me that you are the one who doesn't want kids, and you are the one that has initiated the break up. It's usually the case with these sorts of issues that, if they are resolved, it's by way of the person who originally didn't want children changing their mind. The fact that you have broken up with your girlfriend suggests to me that you don't think there's a realistic possibility of you changing your mind on this. In which you clearly made the right choice, because as much as you love each other, the relationship simply cannot survive if one of you wants kids and one doesn't. For all the positives in this relationship, the better thing is for the two of you to start looking now for partners that share your view on having children.