I remember learning this one - no article should be specified when describing someone's profession when using the verb etre, http://french.about.com/od/vocabulary/a/professions.htm
At least you can consider that when talking about jobs/occupations, article are unnecessary
I want to say no, only because, in European Portuguese, we can say both «doutor» and «médico» as well.
But you can say "Il est un prince" or is it because it is not really a job so that's why it got the article
"Doctor" isn't a job. Its an academic title. "Physician" is a job. Chiripractors are doctors, pharmacists are doctors, The highest level in nursing are doctors, anyone with a PhD in any science, even philisophy are doctors. People attain the title of Doctor but in no way does it make it their job.
Dr is the job title in the UK. We don't use physican when refering to doctors.
It's the same situation in German. You "are physician" (no article), but "a prince" (with article). The reason is that saying someone "is (job title)" is the short form of someone "is (job title) by profession". So "being prince" would imply that you are a prince "by profession". And that sounds very weird. I think it's the same thing in French.
En France "docteur" est un niveau de diplôme, pas un métier. le terme docteur est parfois utilisé à la place de médecin (en réalité docteur en médecine) mais c'est une erreur car un docteur en droit ou en lettre n'est évidemment pas médecin. Est-ce la même chose en Anglais ?