Queensland, Western Australia and the Northern Territory do not observe daylight saving, so from October onward those three run an hour behind the south-eastern states. 13 October 2029 falls inside this seasonal clock split, which lasts until the following April when the south-east moves back onto standard time.
A public holiday that falls on a Saturday sits inside the weekend rather than beside it, so it does not automatically create a substitute day off during the working week; whether one applies depends on the specific holiday and the state. Saturday 13 October 2029 falls on this day of the week, inside the weekend itself.
A public holiday that falls on a Monday or a Friday produces a three-day weekend without using any annual leave, which is why long-weekend planning around 13 October 2029 depends on which day of the week the nearest public holiday falls on. A midweek holiday delivers no such automatic extension, though many workers bridge it with a single day of leave.