Hi LuckyJinx,
Here's what I did:
My wife and I opened all of our utility accounts and telecom accounts under both of our names. Our lease was also in both of our names (with a very large property owner). I'd suggest you start by opening accounts in this manner if you haven't already. We opened these accounts after we were married, but before my application for PR went in. At the time, I was in Canada visiting my wife under a Visitor Record (6 months, renewed as needed).
I was able to open a personal (not joint) bank account here in Quebec immediately after I received my QSC (Quebec Selection Certificate), about 7 months before I received my COPR and landed as a PR. I know that Equifax had record of me at the time I went into the bank because of the accounts I'd opened with my wife - you can request a copy of your credit file from them which will probably be very short.
When I looked into opening a bank account I was told that I needed to bring my QSC, Passport, and Visitor's Record but I ended up bringing my entire immigration file along. I also brought a list of all of my U.S. bank accounts. I can't remember if there was anything else they needed to see when I met with my advsor at RBC.
I was offered a Visa card when I opened the account - it had a very low limit, but by using it I've been building my credit here bit by bit. We use it for regular expenses and pay the balance each month.
I don't know if every bank out there has a program for opening an account in this manner. A few people I know expressed surprise that I was able to do this before landing.
With this said, you should have an easy time establishing credit and opening a bank account, as you already have an SIN card and a work permit.
Best of luck!