For the charger - don't bother buying an australian psu just for a 20-day trip, it's not worth it. Find one of those switchmode multi-voltage plugpacks that is 100-240V compatible; they should be pretty easy to find in any decent electronics shop. They usually come with a bunch of tips, and one almost always fits the Z. Then you can just use a cheap wall adapter to allow it to plug into australian sockets.
Oh - make sure it's switchmode (if it's big, boxy and *heavy*, it isn't) and make sure you get the tip polarity *right* (tip positive) or you'll blow fuses in your Z's charging circuit.
Hotspots aren't very widespread here - it depends on which city you're in though. And they can be quite expensive to access. I've been saved on occasion by a nearby Gloria Jeans Coffee that did free-with-purchase hotspot access, though (even more so when I discovered the password slips weren't one-use-only like they claimed to be ... )
As for the batteries, you might try amazon, they seemed to have a limited quantity of cheap ones (no good for me since they wouldn't ship outside the US.) Failing that, it seems that the external PSP battery packs use the same voltage and plug as the Z, if you don't mind juggling two boxes instead of one. And they're probably readily available everywhere. See the discussion at
https://www.oesf.org/forums/index.php?showtopic=11839 for more details. There's even some talk about the other external battery solutions in there as well.
