I would try to have a test to confirm the father as soon as possible. Two reasons- you'll want to genetic history of the father for health reasons for the baby -and if you are hoping that the father will participate and support you they may be reluctant under the circumstances unless you can prove paternity. Good luck
She won't get the genetic history of the father unless he's willing to tell her. I'd have loved to known if there was anything with my OH's family, but since he was adopted we know nothing. Your making it sound like that because she doesn't have this information that there may be problems with the baby. I had my 20 week scan a couple of weeks ago and everything came back normal, and a lot of physical handicaps are picked up then. There is no guarantee that they have missed something, or it may be mentally handicapped in any child regardless of the parents genetic history.
nicole I would wait until the baby is born for a DNA test. I know you'd love to find out tomorrow, but you can't. But as you said although the risk is low, there is still a risk and that you'd rather not take.