Thank you for your question. To Introduce myself I am a sydney based Solicitor and will do my best to provide you with relevant information to assist you.
The visa you need is a Subclass 600. If you apply for 6 months when you are outside australia you have to be outside when the visa is approved.
If you enter on an electronic visa you will get that automatically when you enter but you can only stay for 3 moths. You can then apply for an extention of 3 months before the electronic visa expires.
You will need to remain in Australia until the 600 is approved.
The following link provides you with the relevant information.
You can download the form online and then you can post it or deliver it to the authorised department.
Depending on the country you are in when you apply will determine where you lodge the application if you decide to apply for the 600 initially.
You should have your insurance with just in case something happens. The authorities will not necessarily ask for evidence of it but you should have it.
I cannot say how long it will take. It depends on where it is lodged and how busy they are. They will give you an indication when you lodge the visa.
Is there anything else I can assist you with?