For the FHOG itself, it's a fairly straight forward form. The supporting evidence is essentially certified copies of ID. All of this needs to be original ink (you can't scan and email it).
Easy enough to download the form, fill it in and post it to the lender or broker. The Australian consulate can certify the ID.
None of this is really difficult, it's mostly a logistics problem. Just make sure there's plenty of time to get things sorted, such as a 60 or 90 day settlement.