I'm only seeing this now, a bit late! But
1) as Nicki says, NEVER sedate dogs for transport; this is dangerous for animals during flights, especially short-nosed breeds. It is important to start to work to crate train her now so that a crate is a calm and happy environment for her. I doubt you'd find a knowledgeable vet who would even be willing to sedate an animal for a flight though.
2) dogs CANNOT go in the main cabin under a seat, to Australia. They must go in the hold; the whole quarantine process is very strict. So as EddyAnne says, get a very very good transport company or make sure you build in all the time you need to have her fly on your flight if that is allowed (it was for me to bring dog from the US to Ireland, via Heathrow). Be prepared -- the cost is likely to be *at least* 2-3 times your one way flight ticket and maybe much more, if she is not flying the same flight as you. I had to have her to the airport FOUR-FIVE HOURS before the flight as there's a lot of paperwork and they have to seal the crate (eg with a locking plastic band so the crate cannot be opened). Also be absolutely sure you have an adequate, officially-acceptable flying crate.
There are cavalier breeders in Australia so the breed is able for the climate. But you want to make sure a dog always has access to shade and water and isn't overexercised in heat or overexposed to it.
I flew an older, crate trained cavalier transatlantic San Francisco to Heathrow and she seemed happy enough at the end of it. I have also flown three of my dogs on shorter routes (UK/Ireland).
My advice is to get and review all the documentation; ring the embassy in Ireland for help and advice; talk to the correct office by phone in Australia... also your airline will probably provide checklists and directions too (which I reread tons of times yet still almost failed to get a needed stamp due to ambiguous phrasing). I still found the airline's materials easier to follow than what was on the USDA website... however if you fly with a good transport company they will look after all this. I know there is a crowd in Northern Ireland that do animal transport internationally; don't know anything about them though.
There's advice on crate training in the Library section here. Feel free to PM me with any further questions as I am also based in Ireland.