The aircraft departed Brisbane for Cairns at 0343 UTC, cleared at FL330. This level was coordinated by the Brisbane Sector 7 Procedural Controller to Townsville Control. At 0435 UTC, the Sector 3 Radar Controller contacted the Sector 7 Radar Controller requesting a level change for the aircraft to FL350. This was approved and the aircraft was recleared at FL350. However, the level change was not coordinated with Townsville Control who were still expecting the aircraft at FL330. At the same time, the level change was not recorded on the flight strip for the aircraft. The request from Sector 3 concerning the level change was not heard by the Sector 7 Procedural Controller as there is no facility for that person to monitor the radar controller's hotlines.