Actually the money is available on your casino account even though the money didn't leave your bank/credit account yet, what is happening when you make international online transaction using your debit/credit card is this.
The casino or sometimes the third party asks your bank-not in person, between servers(computers)- if you have enough money to pay the casino and the bank is happy with this transaction, and the bank says yes and the casino is notified the banks says yes, they put the money into your casino account even though the casino didn't get the money yet.-I explained this in a long sentence, but this communication between the casino/the third party and your bank takes only a few seconds. Your available balance might be shown as $100 less on your bank/credit account as soon as you push "deposit" button, that is because the bank holds the money to send, not because the casino already got the money.
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And normally the banks hold the money for a while, and it go through a few cyber space and it lands into the casino in 1-2 days normally but sometimes much longer.
What the casino says is, the money from Australia cannot come into their casino account, they don't see the money from Australia, so they need transaction ID to trace down.
Online transaction especially international online transaction is different from when you go shopping locally-you walk to Woolworth and buy a milk and pay by your debit card, as soon as you push "ok" button on eftpos machine on Woolworth, the money leave your account right away and goes into Woolworth account, but international online transaction doesn't work in that way.
I know it is hassel, but why don't you ask your bank for transaction ID like the casino asked, also ask the bank to trace the transaction for you. If the money didn't arrive at the casino, it is possible the money is somewhere in cyber space and it can be tracked down if you have transaction ID.