Suggest you start here and gather your facts.
Human Rights and Equal Opportunity Commission Website
Employers can ask for your background history but you have the right to decline to provide it ( you may not get the job).
That said you also have rights to privacy and in many cases some "criminal" history may not need to be disclosed. All I can suggest is that when an employer hands you forms to sign for them to run a check you should ideally take them home, read the wording carefully and if possible call the authorities that will be providing this information and ask them what they will indeed be providing the employer in return.
In many cases drink driving is often not mentioned in criminal history checks to employers unless jail term accompanied the offence. Alternatively applying for a bank tellers job having been convicted of armed robbery would in all liklihood be disclosed.
Good luck