Alot of people don't plan for that long jet lag, so you're doing the right thing. Heading West isn't quite as bad as heading East, and the older you get, the tougher it is. But I can somewhat relate to your long journey. We flew from Washington, DC to Los Angeles and then to Tahiti. Got up at 4:00am and by the time we got to bed, it was about 26 hours later. So leaving from Australia would definitely prove to be tough on the body. It would be great if you can plan a stop half way, but sometimes time does not allow it.
As for April, plan to dress in layers. It can be cool and it can be wet. So take some long sleeve shirts, a few sweaters, and a good rain jacket. That way you can pick and choose depending on the weather.