Québec has their own immigration System. It's a different system. People always try to avoid Québec for immigration due to the complicity of its immigration System. You could look at Québec as a different country within Canada. Even if you apply for refugee in Montreal, Québec and got accepted, you need to obtain a Certificat de sélection du Québec (another application- it take 6 months-one year) then you can apply for PR there.
The length of time it takes to get your hearing depends on whether you made your claim at a port of entry or at an inland office. Also whether you are from a Designated Country of Origin (DCO) or non-DCO. For refugee claims made after 2012, the government's goal is to have hearings within 60 days for inland, non-DCO claimants (shorter for DCO claimants), regardless of your location within Canada. I know some claimants who have had their hearings (in Toronto) postponed beyond that 60-day target. But that doesn't mean that there aren't similar postponements in the other cities where IRB hearings are held (Vancouver, Calgary, Winnipeg and Montreal).
Here is a link that explains DCO/non-DCO, and the time-lines for each.
