Happy birthday and congratulations on your present!
If you don't have a credit card, you can always pay using an Amazon electronic gift card/certificate, which your dad can purchase on his CC and send to your email address for you to apply to your own Amazon account.
I think you have to buy it in US dollars since the Kindle store charges in the same, no matter where in the world you are located when buying your books.
Also, using a gift card means there are fewer small charges to the CC, which can be an advantage if you buy an additional gift card when the exchange rate is better and pay any currency conversion charge only once.
There are many time-limited promotional free books available on Amazon which you can "buy" without having any credit or gift card balance in your account. The sticky thread FREE (and very inexpensive) books for the Kindle
at the top of this forum tracks new ones as they arrive, and Jungle Search
has an automatically updated list of them all, when you scroll down to the bottom.
Amazon has recently eliminated some (but not all) of the Whispernet surcharges for international users, at least as far as promotional free and public domain books are concerned. Even so, not all the "free" books will be completely free in Australia now, so please remember to double-check the price and make sure it says $0.00 before 1-clicking any that you are interested in.
Hope this helps.