In the Anglosphere we've traditionally been quite wary of national ID databases for our own citizens, for better or worse.
Most governments of foreign countries I have visited (US, many parts of Asia) have my fingerprints. The Australian government doesn't (to my knowledge, anyway).
Any Australian with a driver's license or passport most definitely has their facial biometrics stored. Any visitor to the country also is subject to it.
This has been in existence for over a decade and I'm astonished people aren't aware of that.
Right, I do know that (The Capability(tm)!) and for some reason I just mentally exclude facial recognition from the term "biometrics". OP specifically said "at least fingerprints" - it's good to have a reminder that facial biometrics still count as biometrics too, and they're lower on the hierarchy than fingerprints.
From my experience going from clean shaven to a small beard can throw the whole system off and requires manual intervention rather than going through the automatic gates. Fingerprints surely would be more accurate.
Have no idea whether foreigners have to give fingerprint scans at Australian customs, it's common practice throughout Asia.
I live in Spain and they take your fingerprint when they make your ID card. I'm pretty sure that goes into a database, so they have the fingerprints of all citizens.