Cathay Pacific does not fly first class into Australia any more. The 'most luxe' option would be Qantas first class from LAX or DFW. Qantas business class on the A380 also has fully-flat seats, although I'm not claiming that's better than Cathay Pacific.
As mentioned above, you can book 331 days in advance and the seats in J & F sell out extremely quickly, if they even survive to the 331 day mark after Qantas people pick over them.
What is in your favor is flexible dates (that is the impression from your posting, anyway).
My suggestion would be to look as early as possible in your window. You don't say how long you are looking to go to Australia for - 2 weeks? 2 months? The closer to Christmas you try to return, the more difficult your task will be. Therefore, if you're able to book in October/November, I'd suggest you figure out your plans quickly and start looking at the 331 day window.