As far as Canada goes, yes you will have to pay tax in Canada. I am not sure how it would be calculated in Australia. I am guessing you'd have to claim some tax credits in one country for taxes already paid in the other country.
This is right. Foreign tax credits can be a real PITA if the CRA decides to investigate them (which they frequently do). Especially with a country like Australia that does not have a calendar year tax year.
It is easier if the OP can get his "employer" to treat him as a self-employed contractor.