Co-ordination was received by Darwin Control from Unjung Pandang for VR-HOZ tracking via air route A461, advising its estimated time at BUTPA and that it was maintaining FL330. The level was read back by the Darwin controller, who then co-ordinated this information to Perth International Flight Service Unit without advising the flight level as this was not required by standard procedures. The Darwin controller then requested information from Unjung Pandang on V8-RBC, inbound to Darwin on air route B583, which is a converging route with A461. V8-RBC had an estimated time of arrival at the ELBIS position within 10 minutes of the estimated time of arrival for VR-HOZ at the BUTPA position. This required that both aircraft be vertically separated by 2,000 feet when they arrived at these reporting positions. In sequence V8-RBC and VR-HOZ positions for ELBIS and BUTPA were co-ordinated by Perth International Flight Service Unit to Darwin Control, advising that both aircraft were maintaining FL370. Darwin Control queried the level of VR-HOZ and asked that confirmation be obtained from the aircraft. As a precaution V8-RBC was instructed to descend to FL350. Darwin Control contacted Ujung Pandang who confirmed that VR-HOZ was maintaining FL330, but when contact was made with the aircraft the pilot advised that they had been cleared to FL370 by Manila while in Philippine airspace. Although the incorrect co-ordination received by Darwin Control resulted in the required vertical separation not being maintained, the aircraft had not come into close proximity of each other when vertical separation was re-established. Safety Action: The Civil Aviation Authority have issued a local operating instruction at Darwin which requires flight levels to be included in co-ordination between Darwin Control and Perth International Flight Service Unit.