Q1: How long do you plan to be back in Australia for?
Q2:Do you already have a Thai bank account in your name only?
If you answer yes to question 2, you can apply for the Non-O inside Thailand, but as
@John *********
said, you'll have to stay in Thailand until the visa is approved. If you answered no, then you should apply for the visa in Australia, through the Thai Consulate if you will be in NSW, or the Thai Embassy if you will be anywhere else in Australia. Then when you return to Thailand and open a Thai bank account in your name only (if you don't already have that), and deposit your 800k+Baht asap. The initial Non-O Visa allows you 90 days stay upon entry. As soon as your 800k Baht has been sitting in your Thai bank account for 60 days, you can go to the nearest Immigration Office and apply for a one year Extension of Stay.
Applying for the Visa in Australia, you're probably going to need to allow something like two weeks for the approval.
Opening a bank account in Thailand now, is pretty much impossible unless you have a long term Visa, such as a Non-O