If you think ethics is the study of the question "what should we do?" then metaethics is the study of the question "how should we determine what we should do?"

Ah, I think the characterization 'ethics of ethics' or 'physics of physics' is misleading then: you don't mean a physical theory of physical theories, or an ethical theory of ethical theories. This makes it sound like the meta-study asks the same questions as the object level study, only about the object level study. But I take it you mean that the meta-level study asks different kinds of questions; in your example, meta-ethics asks epistemological questions about ethics, while ethics asks ethical ones about the immediate objects of study.