I'm very close to telling my girlfriend that our relationship will be over if she doesn't want another kid in the future.
Why would you want to end your relationship over that?
I don't want to live with a empty family. I want a big family.
It is understandable that you wanting more children is something that you don't want to back down from. It is good to be honest with her so she knows what you really want from the relationship and she can make a decision based on that.
I figured that my girlfriend will not be open to the idea of having more children and after that I'm going to tell her that we are done.
You shouldn't go into the conversation with this mentality. You should have the conversation first and have her see your side of things. You never know she may be receptive towards having another child.