Can a healthy 43 year old woman still have a baby?

Yes but. Be aware that any medical issue that you have during a pregnancy may need to be managed differently.(medication effects on fetus, etc.) your risks of an unexpected outcome (cleft, premi, infection, etc.) is a baseline of 4% plus any additional risk /age (down syndrome=1%) . Mom had my little sis at 42 & thinks it's one of the best things she did.