The work in Western Australia will not be a problem, because of the dry heat. You're hair will dry pretty quick out in the sun. The problem with sweating that much will be that your head will itch like no itch you've ever had before. It'd be best to wash as often as possible. Wash once and see how long it takes to dry. If it dries within the work day, you could probably get away with washing every other day. You'd itch a bit for a day, but not as much as if you let them go without washing for a week.
As for Costa Rica, the humidity will slow down your drying time considerably. If you are planning on getting your hair wet every day, though, rinse them off with fresh water after you are done for the day, and use a blow dryer to help speed up the process. Don't do your normal washing routine as often. Maybe once every 4 days to once a week. I don't know from experience how long they take to dry down there, but I know that it will take longer, because of the humidity.
You'll find out what works best for you when you get there and wash for the first time. Just keep an eye on how long it takes, and work from there.
Also, it Australia, you might want to think about wearing a hat. That much sun all day long could damage your hair. UV radiation doesn't just hurt your skin.
In the tropics, wear your hair down as much as you can. You want as much air flow between locks as you can get so they dry as fast as possible
