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Are Australian citizens allowed to live in Canada for 1 year? Is it hard to get the appropriate visa's etc?
Australians fall under Canadas eTA (Electronic Travel Authorisation) program, which would grant you up to 6 months stay as a visitor (the eTA could be limited to less time than that).
To stay longer than that, you would need to apply for a temporary resident visitor visa, which you can do in-country during your initial stay.
I wish to keep my existing AU job (i.e. all salary goes into my AU bank account, I keep paying AU tax) but I will be physically doing my work in the country. This means I won't be stealing a Canadian job from a local.
This is acceptable to Canadian immigration:
What kind of activities are not considered to be “work”?
An activity which does not really 'take away' from opportunities for Canadians or permanent residents to gain employment or experience in the workplace is not “work” for the purposes of the definition. Examples of activities for which a person would not normally be remunerated or which would not compete directly with Canadian citizens or permanent residents in the Canadian labour market and which would normally be part-time or incidental to the reason that the person is in Canada include, but are not limited to:
...
long distance (by telephone or Internet) work done by a temporary resident whose employer is outside Canada and who is remunerated from outside Canada;
You should be fine working for an Australian company while in Canada on a non-work visa.
Can my child or children go to a school over there?
As you would be a temporary resident (under an eTA or a Temporary Resident Visitor visa) your child may need a study visa of their own to study in Canada:
It should be noted that minor children of a temporary resident (visitor) who is not authorized to work or study require a study permit to study in Canada.
However, this is contradicted further down that same page:
If the parent in Canada has valid temporary resident status as a visitor and is authorized to work or study without a permit as per the IRPR, their accompanying minor child in Canada is authorized to study without a study permit at the pre-school, primary or secondary level as per subsection A30(2)
Get a lawyers interpretation of that!