Can you get a DNA test for a baby you're expecting?

yes it is

@Winters That’s crazy. Do you know how they do it?

Look here, its normally for prenatal paternity test, they either take some of the amniotic fluid surrounding the baby or taking cells.

link

They will also test for potential genetic and/or chromosomal problems such as Tay-Sachs, Downs, schizophrenia, etc.

Since my wife was over the age of 35 when she was pregnant, and because I am a carrier of the most common genetic mutation associated with cystic fibrosis, we had amniocentesis performed during her first pregnancy. It showed that my daughter is indeed a carrier. This is information that will help her in the future. My son is not a carrier, which is good.

The procedure carries some risk of miscarriage. Maybe half a percent. They usually perform these procedures at between 16–18 weeks, if I remember correctly. I seriously doubt you have an risk factors that would make such a test something to consider.