Okay so: the Airbnb is fine, is well equiped, spacious and can hold the heating during winter. It also accepts pets, even though we decided not to bring ours. The neighborhood is super cute, full of restaurants and there is a big market not far from there.
However, *IF* you are going during winter without a car and/or is a light sleeper, this is not the best choice for you.
The apartment is on the 1st floor and the walls are extremely thin, so we could hear people walking all the time and water running all the time. Besides that, the spring bed is noisy with the slightest movement and the whole place has thin curtains.
Now for the winter without a car, the 15/20 minute walk turned into 30/40 during winter because Quebec is leveled. So there is a lot of slippery stairs and steep streets to reach Old Quebec. This one is on me though, I should have made more research about the city because I am not from there - still, useful to know.
Other than that, good stay and good hosts.