Well, if the child is only one I would say go ahead and let the baby meet her friend. I wouldn't suggest teaching the baby to call every guy she dates "Daddy". If she really likes this guy, and he isn't just a fling he should realize that she has a family, and let him know that her baby is the most important person in her life.
I would think it would be hard for someone to try to start a new life with another man, but, it has been done many times before. Just make sure that the man is really good with children, because she is also looking for a person who might eventually become more that a boyfriend. Make sure she lets her boyfriend know that her baby is the most important part of her life, and she needs to know he isn't a scumbag that would ever harm a child emotionally, or physically.