I'm not much help with the flying aspect as I haven't flown with mine [yet].
But I do believe that the 'carry on, medical equipment' is correct.
If you want to actually use it on the plane then that can be done, but you need to check the specific airline rules on how you can do it.
The power points shown by justMongo are correct as well, 220-240v 50Hz
I think most CPAP power supplies run on 110v to 250v systems as long as you have the appropriate adapter to fit the socket, but check your machine specs to confirm the voltage range it accommodates.
As for the humidifier, check the average weather conditions for Busselton at the time you are coming here to see if it is in the same range you experience during a year in your home location, if you don't normally use the humidifier under similar conditions then don't bring it if you don't have to.
There is an Australian CPAP support group on Facebook, you may want to join the Page to get more specific advice on what you need to know.
I will be flying with mine in the future, so will be interested to see how you go.
My flight out will be day time [to the Philippines], but the return flight is an 8.5 hour overnight trip, though I think I would not bother to use it on the plane as I can skip using it for a night and still stay compliant for my driving licence conditions.. I just can't skip too many nights.
I hope you have a great time here in Oz.... once you have been here I'm sure you will want to come back again and again.