Two aircraft, at the same level on air route A585, lost separation standards assurance when the controller did not apply the appropriate standard. The lead aircraft was a RAAF VIP Boeing 707 carrying the Australian Prime Minister. The trailing aircraft was a scheduled Qantas passenger service. The Brisbane Sector 12 controller applied a 10 minute separation standard instead of a 15 minute Oceanic standard when he allowed the lead aircraft to climb to the same level as the trailing aircraft. Later, the controller assured Perth Sector 1 controller that the 10 minute separation standard would be monitored and a distance standard established if necessary. The separation was reduced to eight minutes at Port Hedland when the lead aircraft, Aussy 360 arrived one minute later than ETA and QFA10 arrived one minute earlier than ETA. The controller did not establish a distance standard (20 NM on DME or 30 NM RNAV) when the aircraft entered the CTA, 120 NM north-west of Port Hedland. The controller applied an incorrect separation standard of 10 minutes to the aircraft at DOMOM whereas the oceanic standard was 15 minutes. He also did not establish a distance standard between the two aircraft as agreed with the Perth Sector 1. The controller could not explain the omissions. However, he was on a late night shift with little traffic under his control. He may have been in a state of low arousal and was unaware of the errors.