Not all of them necessarily have birthing clinics though.
Edit: Per my reply below, Nunavut seemingly has just one birthing clinic, located in its capital of Iqaluit. The realistic solution would be to reopen the former birthing clinic in the secondary major population center of Rankin Inlet, which would be a closer option for those who otherwise have to travel to Winnipeg.
Those in the Kitikmeot Region and northern Qikiqtaaluk Region would still have to travel far to visit the nearest birthing center, but as the particularly sparse population of those regions of Nunavut make additional centers unviable (given the difficulty in just servicing Rankin Inlet), the proposed solution of local midwife services would be viable for births without anticipated complications.