Am I being unreasonable

I agree with Riverwalk you are clearly not the breadwinner so go on the holiday. You are being unreasonable in not consulting your manager or giving any thought to colleagues who may also want time off.

As someone who has been an employer and had to manage staff absences, I am afraid that my sympathies are with your manager. I would have been angry if one of my staff had made such arrangments without prior consultation with me. This has nothing to do with wishing to spend Christmas with your family, it is to do with your contract, a contract which you signed when you took on the job. You should have discussed this first, explained about the other staff being willling to cover your absence, and then asked if it was ok to book your ticket, not presented your manager with a fait accompli. You have two choices, either go to Australia, enjoy your Christmas and take the consequences on your return, or look for another job now, making sure you tell them about your Christmas plans. I am sorry if this is not what you want to hear, but having family overseas is not grounds for breaking your employment contract.

I think the best solution to this is for the OP to hand their notice in on 1st November, I assume she has to give one months notice when she wants to leave. She has then left her job well before your holiday date.

There will be no disciplinary issue and she will not be sacked so that if she goes for another job her current employer will give her a neutral reference. Put the issue to the test and any reference will in some coded or direct way state that she left her current employment under a cloud, which will do her re-employment chances no good at all.