You do not need to pay duty on personal effects when you move to Canada, as long as you meet the criteria set out by the Canda Border Services Agency, which is;
You must have owned and used the goods for 6 months or more before your move to Canada
The goods are for your personal use, and not for commercial purposes
You ship the goods within a year of your own arrival date
There are some exceptions however, including alcohol and tobacco products above certain personal exemption limits, motor vehicles (more detail on this here) and new or unused items, which could attract further cost of duties and taxes when moving to Canada.