Should I stop her?

I just got into a new relationship with a girl. She is a single parent of a son who is 4 years old. She is a school teacher, has a degree but lives in a one bedroom apartment. We went out and we ended up having sex but we did not use protection. She is now telling me that she is feeling cramps and her period is not coming. She tells me that she is scared that she is pregnant. I told her that its ok and whatever happens we will figure it out together. She said that if she is pregnant she wants to have an abortion because she is not ready for another child. Besides this we do not really know each other well and that we are not really serious. I told her that I do not believe in abortions and that I know that we were not dating for a long time but if she decides to have the baby I will stick with her no matter what and that we are two working adults and although it could be difficult we can make it work. She still says that she wants to have an abortion if it turns out she is pregnant. I told her don’t think about that too much and whatever decision she makes I will be behind her. My question is, if she is pregnant should I stop her or talk her out of having the abortion? Will I be a coward for not doing so and helping her with the abortion? Also, am I wrong for trying to talk her out of the abortion? Is this entirely my fault? Am I unfair to want her to have a child that she does not want?