My question involves paternity law for the State of: Virginia

My boyfriend and I have been together for a year and a half. Before he was with me he was dating someone who cheated on him with at least four different people. She refused to do a paternity test when the child was born, so my boyfriend refused to help her or take responsibility for the child. Now, almost two years later she is bringing the subject up again because she needs money. We don't want to deal with it because he has moved on and we are engaged. However, I know there isn't any avoiding a paternity test. My question is, IF the child is his, how likely would it be that we could take it away from her. We have both decided that if it is his, she will be allowed contact but we do NOT want HER raising his child. I know there is some consideration when the child is under two and it is easier to win. We could honestly give the child a better life than her. She works at a low end job and leaves the child at a babysitters. There are some concerns about more personal problems with the household but I'm not going to get into that. My boyfriend and I both have great jobs, he just got his bachelors in computer science and I work in the veterinary field. We work different shifts and days so there would always be someone to care for the child. And we have full support from his parents as well who are certified foster parents and respected members of the community. So tell me, what are the odds?

Thanks!