I was also thinking this would be related to DST. The "tricky" bit about Australia is that DST is "backwards", at least compared to those of us in the northern hemisphere. Because the seasons are reversed from those north of the equator, DST is also likewise reversed. They spring forward in October, and fall back in April. It all should make sense when you think about it. (Longer days are still in the summer, and thus DST is still in the summer.) This is of course not unique to Australia. (I think they just happen to crop up probabilistically by having a high population using technology, and are south of the equator.)

The cool bit, at least to me, is that the mnemonic "spring forward" still works. Likely, this is only cool to me because the whole thing is unusual.

The other odd bit is that some TZs sit on the "wrong" side of the international date line, and thus get interesting offsets such as +13 or +14h from UTC. I think there's some that are -13h too, so the total "length" of day (that is, how long you could remain on a calendar date) is >48h. Thus, at any given time, people in their local time are in as many as three different calendar dates.

There's also a few TZs with half-hour offsets. (e.g., they're something like 4.5 hours off UTC.) There's a 3-hour TZ jump at one point on China's border, I think, because all of China is on a single timezone, and the nation is quite wide, east-to-west.

We've not even gotten to leap seconds, or that 2100 won't be a leap year.

And governments regularly muck with this stuff. The set of timezones and their offsets and DST preferences are constantly changing.