Should I register my brand in other domain extensions?

Defensive registration is cheap insurance, but it has no natural limit, so decide on purpose rather than by anxiety:

• Register the obvious pair - the .com.au and the .au for your trading name, so nobody else trades on it.
• Add .com if the brand travels or if the name is genuinely attractive to others.
• Redirect them, do not park them - an unused domain that resolves to nothing is a wasted asset.
• Publish null SPF and a rejecting DMARC on each - a registered domain you do not send from is still forgeable.

Beyond a handful, you are buying peace of mind rather than protection. Trademark registration does more than a hundred domains.