"That person is our doctor."
You can't say that. You're literally saying "That an is our doctor." In Chinese, measure words are the equivalent of "a" and "an", which signify the amount, category, or the type of the "subject" or "thing." i.e. "A teacher. 一位老师." In Chinese, just remember that measure words always come before the thing itself. The correct phrase is 那位人是我们的医生."