One option you could consider if you go out to Tadoussac is to head up Route verte 8 into the Saguenay and go counter-clockwise around Lac St-Jean. When you get to Chambord, hop on a train (~C$40+$25 for the bike) to Rivière-à-Pierre where you connect to route 6 to Quebec City. The train ride is pretty interesting as it passes through hunting lodges and rustic camps only accessible by rail.
The Trans Canada Trail is an often misunderstood concept — while it is a contiguous facility, not all of it is cyclable. Some segments are hiking only, some are even canoe routes. It's not really designed to be an end-to-end route unless you switch your mode of travel.
There are many roads between Ottawa and Kingston, and if you go parallel to the historic Rideau Canal system, the lock stations allow camping (~$6 per person), most of them have flush toilets but no showers (you can always jump in the river )
The New York State side of Lake Ontario has way better roads for cycling than the Province of Ontario. Getting through the urban mass of Toronto and Hamilton can also be pretty hectic and circuitous. Depends on what you want to see and experience, I guess. If you've never been on the Erie Canal trail, it is such an important piece of American history, and an interesting contrast to the Rideau Canal. There are ferries between Kingston/Wolfe Island, ON and Cape Vincent, NY that are way more convenient than the bridges.