What new laws in Australia are you referring to? I did a quick search and I saw a lot about anti-spam laws (which is great), but how does that affect switching your own domain to fastmail?
As I understand it the oversight is relatively minimal and any company operating on Australian soil can be subject to such a request. Here's their government web page on it: https://www.homeaffairs.gov.au/about-us/our-portfolios/natio...
It passed around the end of 2018 and a lot of Australian companies (e.g. Atlassian) were not fans of it.