Can I file a trademark application that covers the whole world?

There is no such thing as a global trademark application.  There is an international trademark treaty called the Madrid Protocol, which Canada is presently slated to enter in 2019, which does provide a streamlined international filing process.  Until Canada fully accedes to that treaty however, it is necessary to file your trademark application in each country in which you wish to protect your trademark.  It is also possible on a regional basis in certain cases to file a trademark application which protects you in a number of countries – for example in Europe is possible to file what is called a CTM trademark application which does give you the ability to provide or secure regional level trademark protection for your trademark throughout Europe.