Continuing on the correct information that Ozzie Mozzie said,
Some convictions (serious ones such as murder, rape etc) will never be regarded as a "spent" conviction.
The time limit on spent convictions varies depending on what the offence was and amount of time in jail (if any jail time). The information is readily available as people need to know what they have to disclose to prospective employers. Look at the ASIC website, not sure what gov't dept. and all the info you need will be there.
In regards to the DUI, probably no major problem. Im not sure about these days, but 10years ago a drink driving conviction was in fact a conviction on your traffic record, not your criminal record. From memory, I think most states wipe people traffic records after 5 years or so. The chances are that the drink driving record probably doesnt exist, except for court records....I dont think they are ever wiped.
But make sure you check all this info out for yourself....dont trust me!!!!
Eternity.