On a work permit, you are allowed to carry the US registration (License plate) and insurance for 3 years in Canada. So, you do not need to do anything to bring your car to Canada. I had done a bunch of formalities around shipping my car while moving on a work permit from US to Canada and was given the above information by the authorities at the border crossing. All my documentation was a waste of money.
You also have the option to get it registered in Canada if you wish to.
You must inform your insurance company about your move and they will update their records for the insurance purpose, and may send you a new insurance card.
Thank you for your information. Lets say if I choose to use my California registration and Insurance for my 2 years of work permit then is it possible to drive car for 2 years on California number plate also California registration are yearly based what if my registration expiring within six month? Do I need to renew registration online? What you did? Did you registered car in canada and got Canadian number plate?