Ben,
While there is increasing focus on the validity of information in resumes I would be surprised if there were many Australian employers that demanded some sort of official verification. Maybe you have just been unlucky. How many employers have asked for this?
Most employers accept things on face value unless there is some reason for them to be suspicious. Of course they also rely on their interviews and reference checks to verify the information. If you have an original copy of your uni results which you can show them at interview I can't imagine many employers would doubt the validity of that.
As for the format of your resume, Australian employers usually expect to see considerably more information than that contained in a typical UK resume. There is no "standard" format but quite a few large recruitment agencies have a preferred format which they are happy to share (because it helps them get the data parsed into their database). As a guide I would suggest you start with your personal details and qualifications, followed by an "executive summary" or a synopsis of your skills, strengths and achievements. Sometime a brief summary/list of the positions you have held, followed by a more details description of your work history. The idea being that an employer can get a concise picture of you as a candidate but there is more detail there if they are interested and want to pursue it further. Finally, referee contact details, although it is common for people to say they will be provided on request. Some employers specifically require a certain number of referees to be provided up front, but this isn't so common in the private sector.
Lots of people put hobbies and interests on their resume. My view is that you should not do this because you never know what biases the person reading your resume might have. I know these shouldn't affect their judgement, but everyone is human
Last but not least, don't list the names of your wife and kids, dog, cat etc!
I hope this helps.
Kevin