So what happens when the crown changes? They change the holiday? Immediately? For the next year? Sounds like a bit of a nightmare.

The holiday is on the official birthday. The sovereign's actual birthday has been separate from the official birthday for centuries, so the holiday does not need to change.

Nah, it's not even her actual birthday. Different countries with the same queen even celebrate it on different days. Presumably it'll be renamed to "king's birthday" but the day kept the same when the monarch changes. Or done away with/re-purposed - there's a general feeling in Australia at least that once the queen dies there will be less support for the monarchy.

If you think that's a hassle, in Japan the calendar changes with the emperor:

https://www.theguardian.com/technology/2018/jul/25/big-tech-...

Australia celebrates the Queen's Birthday public holiday on different dates in different states already.

It’s not actually the queens birthday.

In Australia, many states have different dates for the queens birthday.

So not a nightmare at all.