That would be a strategy worth considering if citizenships in both countries really are your goal, but such a plan would carry a risk if somehow, your Canadian citizenship application takes much longer than expected.
In the event that everything goes smoothly, you should budget a one year of citizenship processing times after submitting your application, so that would be 4 years roughly after you reside in Canada.
Also, for Australian citizenship application, you need to reside in Australia for 4 years as well, and the processing times also take about a year.
So after moving back to Australia (presumably as a Canadian citizen), then you would have to stay in the country without leaving for two years to renew your visa, then reside two extra years before you can apply for AUS citizenship.
Needless to say, this would be about 9 to 10 years in the future if you are really serious about pursuing this (including two years in Australia where you cannot leave the country)
The reason why I brought this up is because I personally know somebody who is in such situation. He became a Canadian citizen, then move to Australia as a PR (after securing an Australian job)
I would aim for one country unless a job opportunity comes up. Once you adjust to one country you will have to move.
The weather isn't great in Toronto from December to March but it can be sunny and cold. The weather is very reasonable compared to other cities in Canada. In terms of sponsoring parents it will take more than 3 years because taxable income from previous years is used and it is also a lottery. Just wanted to make sure you were aware that sponsoring parents doesn't have an exact time frame.