Should I surrender my rights to my unborn baby?

I was seeing a girl that later determined she did not want a relationship with me, because she is seeing other people. She said that she cannot be in a monogamous relationship. A couple weeks later after we were done talking for good, she contacts me stating that she is pregnant. She is asking me surrender my rights to the unborn child. In a couple weeks she is moving to Mississippi. I am in Indiana. I believe she is approx. 3-4 weeks pregnant. I offered her to stay with me and I will continue to work and support them both. She has declined any help from me including child support. In a perfect world, she would decide to stay with me and keep and raise the child. But as I said, she promised that we will never have a relationship, and she is moving states away soon. She wants me to have nothing to do with the child. Since I am not invited to be a part of her life I want to not be involved in any way. At this point in time she is refusing to artificially terminate the pregnancy. I can't help but feel as though I am in a trap. How do I legally ensure that she will not come back years later and request child support after not wanting assistance now? I really need advice, and I will appreciate any I will receive.