Given that St. Jean Baptiste is on a Tuesday, I'd be willing to bet that, if you don't have reservations already, you might have a tough time finding an open spot the weekend of 20-22 and probably the 23rd as many will take a vacation day to extend the weekend to 4 days. Although this might seem early, this is a big deal to Quebequers and that's the busiest camping weekend of the year in the Province.
Personally, that's the weekend I stay OUT of Quebec instead of going into the heart of it. A lot of drinking that weekend. A good friend of mine works in the loading dock at Costco in Gatineau, QC and they can't bring out the beer skids fast enough... they put one out, get in back to bring out another, and that first is empty before they get there and the delivery trucks are arriving so often they are practically lined up waiting to unload. This goes on all day long almost every day of the week prior, and even worse the Friday of... not a word of a joke, I've been there.