Hi, this is Matt, Jeannie's bf replying.
I'm a Dutch citizen. In my 1295 form I put applying from Netherlands and my Dutch address. The type of WP is "other". I guess the same would apply to you since you already have an offer for a postdoc. I brought a Dutch police report. I didn't know if they checked, I just handed in the pile of documents altogether.
I understand you're being reluctant with this, I had the same feeling, but it turned out well. They will conduct an interview and you'll have to explain your job/research, how long, how did you get the job, what kind of contacts you have established with your future boss, do you have place to stay (saying temporary in a hotel while looking for something permanent will do; showing your reservation will help too), what will you do after your contract end, do you have family in Canada, things like that (20-25 minutes).
In addition to the stuff Jeanny mentioned, you might want to take along CV, proof of previous employment, course certificates, PhD diploma (or thesis acceptance letter-I didn't have my PhD yet at that time, I finished but in NL it can take ~1 year for the graduation formality, ridiculous..). I also brought recommendation letters, just in case (talking about paranoid..). If you can think of other kind of documents/emails that can support your answers to the questions above, just bring them.
I had the forms printed out, but also in my laptop. I was thinking in case something went wrong I can just modify and "borrow a printer" from them. I also offline bookmarked the webpage saying that postdoc is LMO-exempt (again, speaking about paranoid, you're not the only one ;D). In the end I didn't have to open my laptop at all.
One thing I remember, in the website they always say something about "Quebec requirement". I've never looked into it because I wasn't heading to Quebec, but here's from CIC website:
If you intend to work in the province of Quebec, you must obtain a certificat d’acceptation du Québec (CAQ) before a work permit can be issued.
Please look into it if you haven't done so..
All in all, I can only speak from my experience, but I hope it helps. Good luck!