It can be so painful when a relationship ends that sometimes we want it back at any price because the pain without it seems unbearable. It might be that the difficulties between you have been so hard for your girlfriend that she has made up her mind and won't change it. Sometimes things that are said in arguments are personally destructive, and once they have been said, you can't unsay them, however much you don't really mean them.
She may have decided to end it a while ago, but not been able to tell you. If she won't talk to you, you can only guess.
I presume you will be seeing her, as you will be spending time with your daughter. It could be that changes in your behaviour and manner towards her could convince her to try at least dating you again. What do you think? As you say, you were good together once, and you will always be parents to your little girl. In general it is better for children to have two parents, who love each other and can get on together.
I suggest you think about seeing a therapist, either on your own, or with your girlfriend if she would agree to go along. You can choose somebody at Finding a Therapist or go to www.basrt.org.uk and look at their list.