I only have a free sub domain since I don't have a credit card, are there sites that allow you to pay without a credit card? Using my free domain now is not bad but the only advantages I can think of are that the actual link will be easier for people to remember - does that really matter if most traffic will come from search engines that just have a text anyway? Surely people don't worry about what the link is, it's about the site content right?
There is a huge disadvantage, the domain do not belong to you. What if one of these days the owner decides to stop the services? Or decides to take back your domain as it is getting popular?
The only advantage I see is that if you are just testing the market with your site without any capital outlay beyond that there is totally no advantage of a free domain name. The domain name do not belong to you and once you get popular, you will find the domain name yanked out of your hands and you are stuck with nothing, all your hardwork would go down the drain just from the savings of a few dollars a year. Since you are in Australia, you could try to get a credit card from your bank, the last few times I visited Australia, you simply cannot do anything in there without a credit card so it should be relatively easy to get one or at least a Visa/Mastercard Debit Card. In any case, if you have a bank account or a checking account, you could buy from Aust Domains http://www.austdomains.com.au/help_billing.htm . Alternatively, with GoDaddy, you can wire transfer money to your GoodAsGold account and you can use the balance to make payments for your domain names https://www.godaddy.com/gdshop/prepayment/wiring.asp?prog_id=GoDaddy .
You however need a credit card to verify your paypal account and fund it if you are not selling anything through Paypal.