People invest lots of time and money promoting their domain name and it takes time to have a well established website. Its important that you make sure you own your domain name. If you did not actually register your domain name (had a friend or someone else register it for you). It would be a good idea to make sure you have control over it and its in your name. I have personally seen it happen where a disgruntle employee happen to register the company business name under his own name/account, and would not relinquish the url after he was fired/let go.
You can check the whois information to see the exact details. If you had a friend or someone else register a domain for you, make sure that you are the Registrant/owner. You can transfer a domain name with any register that you choose, as long as the person listed is willing. If not, they could easily hold your domain name hostage, and this is what you want to avoid.
It is always best to register the domain name yourself and under your own contact information. Basically, you do not want to potentially lose control over your site and lose all your time and money invested into building your domain. Losing your domain name or changing domain names will affect your rankings with Google. New websites tend to fall under an aging delay, and some site get caught in what people call The Google Sandbox.
Changing domain names is essentially starting over again, and it does take time to get everything back where it was before. It can take at least a year to get everything back to where they were before in all the search engines. Granted some search engines may be quicker to change than others, but Google will take you longer.
You can register Canadian domain names with DomainsAtCost.ca (very reasonable prices for .ca domains). Also to register a Canadian domain name you need to have an address from Canada and fill out the appropriate information from the CIRA.