VH-EBR was tracking from Bali to Sydney via route A576 to Curtin (CIN) and then via route T71 at FL330 (33,000 feet). A40GP was tracking from Melbourne to Singapore via T71 at FL350 and estimating Curtin at 1805 UTC. VH-EBR reported over Curtin at 1742 and requested FL370. The duty controller (on Perth Sector 2, the sector responsible for the section of airspace) checked the distance between VH-EBR and a preceding aircraft tracking on A576 (7 minutes ahead at FL370), because he thought they may be in conflict, and then told VH-EBR to standby while weather diversions were considered. At 1746.49, the controller instructed VH-EBR to climb to FL370. A40GP was probably slightly to the right of track due to a previous weather diversion, but the aircraft were on opposite tracks with an estimated time of passing of 1753. VH-EBR reported maintaining FL370 at 1753.33 and at 1753.55 asked the controller what separation existed with the traffic that had just passed down their left side. The aircraft would have been at the same level and about 50 miles apart at approximately 3 minutes prior to the time of passing. Vertical separation did not exist until about the time the aircraft passed. The required standard was vertical separation of 2000 feet 10 minutes prior to the time of passing. The controller did not recognise the confliction between VH-EBR and A40GP. He had been busy in the two hours prior to the incident. 15 aircraft had passed over Curtin and there were many diversions due to weather. However, in the 20 minutes prior to the incident the workload had decreased to a moderate level. The controller indicated that he did not feel fatigued at the time of the incident. He was on his fourth solo shift following three weeks recreation leave. He had completed three familiarisation shifts immediately after the leave but had not been able to work Sector 2 with any more than light traffic prior to the day of the incident. The initial co-ordination received from Melbourne had A40GP at FL310 but there was a level change to FL350 prior to position T71B. The new level had been correctly carried through to all flight progress strips by the controller. The evidence indicates that the controller had a "mind set" that A40GP was at FL310 and therefore below the level of VH-EBR prior to the change of level to FL370 and would not be a consideration. It is possible that a lack of familiarisation in busy traffic conditions on Sector 2 contributed to the controllers error.