Going from middle school to high school in Ontario can be a very easy transition, especially within the same province. Education is managed on the provincial level, and therefore all public middle schools and most private middle schools in Ontario are designed specifically to lead into secondary schools in the same province.
Moving to a different province can be more complicated. Changing from the public to the private school system or vice versa can also add complications. It is best to check carefully with the secondary school you wish to attend to make sure your transition is as smooth as possible. If you decide to stay beyond middle school and go to high school in Ontario, you will have to make sure you have the appropriate study permit, and may have to renew depending on the time restrictions of your original permit. Overall, however, your move from middle school to high school in Ontario should be fairly simple.