What particular law applies here? I'm sure there are quarantine laws that apply to those who actually have certain diseases, but in this case they're quarantining based on the possibility that someone might be carrying one, and I'm not too sure any such law exists, else they wouldn't have let her have her way, and they wouldn't be scrambling about trying to find some legal means of keeping her isolated.
A quarantine is not only for those who are infected, but can be used to see if a potentially infected person shows symptoms while in quarantine.
That aside, the professional, compassionate and less transparently self-serving thing for this "medical professional" to have done would have been to express her objections but comply.
Forbes has a pretty good article on U.S. law on quarantines:
To summarize, the states have the power to impose quarantines, and so does the federal government.