.com.au is terrible. Get a .com
You're just going to have to get creative and change the name slightly. E.g if your business name is XYZ get theXYZ.com or something to that effect.
I have used Zoom for healthcare practitioners which they don't advertise. It does encrypt everything once you pay for this service. I use HIPAA-compliant email with thexyz.com and they also offer a Nextcloud instance which is HIPAA-compliant as well so everything in the cloud is encrypted and secure (nothing is every totally secure). I use Practice Better electronic health records which has a built-in telehealth feature that is encrypted and they just added Zoom support. I'm in the U.S. so all of us have to be HIPAA-compliant which is the highest standards I know of to protect patient data. Not sure what the European laws are but HIPAA is a good bedrock for privacy since it's designed for that.
Self hosting email is a real challenge. It all comes down to reputation at the end of the day. You really want to choose a provider that filters out spammers and only has reputable companies. As long as you are not sending bulk email, thexyz.com may be worth a look as they offer unlimited email aliases.