Doctors do not monitor the pregnancy of female dogs. Some dog owners may take their pets to the vet for ultrasounds to confirm pregnancy but no other tests are performed simply because they are not available.
There has been no study conducted to determine if dogs could suffer a mutation similar to trisomy 21 as they have 39 pairs of chromosomes in each cell. A dog can have a condition similar to Down Syndrome but experts are not even aware of what to look for at chromosome level to diagnose it.
A number of companies offer genetic testing for dogs to screen for potential inherited diseases but a test for a canine version of Down Syndrome does not exist.