In British Columbia, for example, there's the Pacific Post Partum Support Society, which provides support by phone or by text message. A person who is experiencing postpartum depression can connect with a peer who is on the other end of the line. The hours are not 24-7, but it's very accessible.
In terms of more formal counselling, that would depend on how much money you have to access it privately. If you can afford it, then you can get it almost right away. If you need to go through the public system, that can take six or eight months. It depends.