@HopperDash Has your girlfriend actually said she wants kids?
You are running ahead of yourself in my view. Advice you are getting on here is more or less the same as would be given to mother's on here, in the same situation, for once.
You are only 6 months into a new relationship, which must have started very soon after you and your DDs Mother separated?
You should not have told your daughter so much detail at this stage about your girlfriend for starters, as you don't know if this relationship will go the distance and you have started to date again and discussed it with your DD while she is still trying to come to terms with the split between her parents. Her whole world has exploded.
Yes, you have every right to be happy, and you wouldn't be on here if you didn't care about your daughter, but you asked for a female perspective and you are getting it.
I don't know if this applies to you, or not, but as a general observation guys usually find it easy to compartmentalise emotionally different areas of their lives. So in a situation like yours that would refer to children/adult close relationships/ work. Women are much more likely to look at ALL those things and how they interact together.
That is what you asked for, and the replies reflect that. I can't say much that hasn't been said already: your daughter is both grieving the loss of her family unit and very angry about it too; She will feel that her mother abandoned her and that somehow it is her fault, because that's what children do; She will be terrified of losing you too and perceive that you having a girlfriend is evidence that she WILL lose you, because she isn't enough for you, so you can't love her enough and it will be her fault again - (she's only a young teen, so she's not old enough to understand the complexity of adult romantic relationships, nor the different types of love we hold, which can all be held at the same time);
By all means still continue seeing your girlfriend, but please stop discussing it with your daughter. The more you try to persuade her, the more she will dig her heels in. It's far, far too early to even introduce the two of them to each other as the relationship may not last, once you get to know each other a lot better. How often do you and the GF meet up? Or speak on the phone etc?
I would also add that if the GF is pushing you for a child already, then she is sending out red flags already, as she isn't prepared to consider the impact on your DD, or/and she isn't that into you and maybe just wants to find a sperm donor before it's too late for her? If it's only you who wants another child, please think about your motives for that?
Hope things settle, in whatever way is best for you all.