Also : جورج طبيب
Since they used داوود for David, there's also an Arabic version of the name George, which is جرجس (jirjis).
MSA: جورج طبيب
Why not "George Tabib"?
Because Duolingo likes to use some borrowed words or Slangs.
The correct answer sounds a bit unnatural. I guess "جورج هو دكتور" would be more appropriate.
Nope, that is not nonsensical in Arabic. Although you could say جورج هو الدكتور, with a definite article, but that would mean something different: "It is George who is a/the doctor."
I have also learned a different word for doctor which is "ممرض" which from my searching means nurse.