“The immediate counter question is to ask the doctor about their firearms training and certifications, their knowledge of safe handling and storage techniques and their legal liability should patients follow their advice.”
You are absolutely right: doctors are required to pass certification examinations to show qualification to advise patients in their specialty. There is no reason for a patient NOT to question a doctor’s qualification to advise about gun safety.
I believe NRA should have a doctor’s certification course: if the doctor can’t display the certificate, the patient should not feel it necessary to answer any questions.
Why would a certification be reason to feel compelled to answer unconstitutional questions? If the People are willing to cede their rights and freedoms because someone has a "certification", you can bet that there will be sufficient "certifications to ensure all our rights are wrested away.