Why does Canada still have a queen?

Because Britain hasn't decided to abolish their monarchy.

The British have had a monarchy for over 1000 years with only one brief period (1649-1653) known as the commonwealth period. During that time Britain had not only abolished, but executed their King Charles I, however they eventually decided to bring back the monarchy with Charles II (the son of the executed King) returning.

There are many countries in Europe that would have a monarchy today still if it had not been abolished: France, Russia, Germany etc. Britain's monarchy has managed to make it to this modern period for many reasons, one being popularity, two, being that the British people tend to be rational sorts that need a good reason to cause a fuss ("stiff upper lip" "If it ain't broke don't fix it" etc.) and a thrid being that because Britain won both world wars they were able to protect their culture as is (many monarchies were either abolished or downsized during one of the world wars, and finally a fourth being that Britain has never had to face (atleast not in modern times) any power hungry dictater types like Hitler or Mousillin, if or rather when Britain has to deal with a prime minister hell bent on power the first thing he or she will do is try to abolish the monarchy.

It's important to remember that the British monarchy is nearly powerless. Britain is a constitutional monarchy. The Queen is the head of state, this is a real government profession (most every country has a head of state) so if the monarchy is abolished someone else will have to do her job.