Legal Question in Criminal Law in California

The answer would be yes. As your attorney the documents could be obtained on your behalf. Bear in mind that these documents (your criminal records) must be certified by the court.

I doubt that Australia will ask you to conduct the background check yourself. The point of checking is to find information you would prefer not to share. If applicants could gather the records themselves, many would simply leave out the unfavorable materials. This is true whether the applicant does the legwork herself or hires someone else to do it for her. The Australian government is not foolish enough to let that happen.

Note also that anyone can get your records for you. It doesn't have to be a lawyer.

Finally, note that there are a *lot* of different courts in California, and a great many more elsewhere. It makes little sense for Australia to limit the search to the county (or counties) where you lived. You could have been convicted of a crime in a county other than the one you live in. Going from court to court to get your records would be time-consuming and expensive. There are databases that gather this information centrally; that is surely how the authorities will find out what your records say.