Canada has the right to establish immigration policy. If we're giving work permits instead of landed-immigrant status, then work permits are dependent upon a job offer. If that job offer is in Nunavut, then they have a choice - they can wait for one in a better locale to be offered, or they can go to Nunavut. When their residency is done, they'll have their license to practise and they'll be able to travel anywhere they choose to set up a practice, because by then they'll have landed immigrant status.

As for the rest of their family - well, I'm sure many of the doctors who chose to take this route would be bringing their family with them and settling with them in the place where they worked.

Medical students already do this, btw. They choose between several hospitals in different cities and a residency committee comprised of doctors in that hospital offers them a residency or declines them after an interview/application process. Plenty of doctors do not start their careers in the cities in which they eventually set up practice - though plenty more go to a city for a residency and stay to practise there.

We need doctors in specific locations. They need residencies and Canadian experience before being granted a medical license. This way would solve some of the shortage with minimal hardship.