Indeed, people have drama'd a lot about Australia's surveillance laws, but they have little applicability to Fastmail. Additionally, if you are worried about government surveillance, your safest bet is just to be storing your data under someone else's government.
If you live in the US, it's very easy for the US to get your data, and more irritating for the US to ask Australia for your data.
Australia is part of the 5 eyes alliance which automatically shares data between the US/Canada/UK/New Zealand which means it is a safe bet that the US can get this data as easily as it would be on it's own soil.
As an American storing data in Australia creates another problem. The US can't spy in the US on it's own citizens but another country can at the request of the US government and will report everything back to the US.
I would pick Russia or China first...
Or just use protonmail which is designed to offer some protection.
This kinda depends whose radar you are trying to stay off of...
If you are planning to be a terrorist, having data in a Five Eyes country is a bad thing, because the CIA can probably get it easily. However, for your garden variety crime, no, the local police department can't easily get the CIA to get information from Australia for them.
So depending on your threat model, this may or may not be a big deal.
If you live in the US, it's very easy for the US to get your data, and more irritating for the US to ask Australia for your data.