For now, let me clarify what you should include on your resume instead of your date of birth.
A modern resume should only contain your phone number and email address in its contact section, like this:
What If You’re Applying For Jobs Overseas?
If you’re applying for jobs outside Australia, keep in mind that anti-discrimination laws which prevent employers from requesting your date of birth are also in place in the USA and UK.
There’s no need to include your date of birth if you’re applying for roles in those countries.
I’m not an expert on best resume writing practices and laws beyond these three countries; if you’re applying for jobs beyond Australia, UK and USA, please conduct your own research to ensure that your application fits the required criteria.