Coroners or medical examiners are almost always employed by local governments (usually cities). It's often the case that you are required to be a medical doctor, but that isn't always the case and depends on local laws and how competitive the market for jobs is. Here's one possible path: go to college and make sure you satisfy the requirements for "pre-med" along with a minor in law or criminal justice, then take the MCATs and apply to medical school, and complete medical school with a training in forensic pathology. You'll do a "residency" after Med school, perhaps in pathology. By this point, you should already have some ideas of the jurisdictions in which you would like to work, and should be able to know exactly what legal requirements you will need to satisfy. You may have to be licensed, which requires studying for and completing a test or series of tests. You may be required to complete special training administered by the local jurisdiction.
This is an interesting question for a young person to ask. I don't know that your quietness has any bearing on being a coroner, but being observant will certainly be valuable. You must have excellent attention to detail, as being thorough and having proper documentation is extremely important. You will also have to speak periodically with the families of the deceased, so having some sensitivity to that would be good.