Yes, the Bank of Canada has issued currency here since 1935 and it all remains legal tender, however you would be best off going to any Canadian bank once you're here and swapping your old notes for current issue ones. A retailer might give you a hard time with older issue notes.
The big 5 banks in Canada (in no particular order) are RBC Royal Bank, TD Canada Trust, Scotiabank, CIBC and BMO Bank of Montreal. In the case of your $1 and $2 notes, unless you have at least $5 or $10 worth, you will get $1 and $2 coins since our paper money starts at the $5 note.