So...this raises the question: 

What "remote" island do we send them all to?  One off of a coastline, obviously.  I live in B.C.  NIMBY! So, that leaves the Eastern coastline.  Possibilities abound: 

1. Sable Island?  Naw...Parks Canada place; tourists love to see the horses. 
2. Anticosti?  That has possibilities.  Less than 300 people live there, and it's bigger than PEI.  Security would be a problem, though.  It's only a short distance from the mainland, so all boats at Port-Menier would be placed under surveillance. Government would have to establish watchtowers on the mainland, manned 24 hours a day.
3. St. Pierre and Miquelon?  Nope...International concerns--belongs to France. 
4. Magdelen Islands.  Distinct possibility--there are 8 major islands and some small ones, too.  Quite a distance from Cape Breton and PEI.  Population is sparse. Hey...Brion Island is uninhabited!  Oops.  Nature reserve.  Hmm...