Doctor Who is a shape shifter, but what is basic type? It is a diifferent Galaxy from the Terran Empire "S" types and introspectives "N" types form the Jovian planets (sometimes called Foreigners or Aliens). .
But as a Time Lord from Gallifrey, this I assume to be a Jovian planet in their Star System. Time Lords are intuitively thought to be INTP. However, the Doctor is reprobate and he may have regressed to a scatty INFJ.
However, the two hearts put a different perspective on things. He is probably a dual processor operating two types at the same time.