Mosquitoes can start being a hassle in June, so can the black flies. But its not like in Alaska or Yukon, if what I read about those places is accurate. You should be fine to get a place to camp easily enough but if you have a specific area or specific national park you want to stay at, I encourage making reservations. Late May and Early June are great for camping as the kids are still in school so less crowded for sure. We have had rainy springs the last couple of years. Newfoundland can be cold and wet that time of year as well.
Oldcow