Three aircraft were being processed by Brisbane Sector 3B for arrival at Maroochydore. VH-CZB was tracking via position TRIKI (21 NM, 128 degrees from Maroochydore) and was on descent to 6,000 ft. VH-PIE was level at 5,000 ft and also tracking via TRIKI. Another aircraft was on the Brisbane-Maroochydore direct track at 4,500 ft. Seven other aircraft were under the control of Sector 3B at the time. Because of the workload in the sector, PIE had been maintained on Brtisbane Approach frequency, although the Sector 3B controller had a flight strip for the aircraft at his control position. When CZB reported approaching 6,000 ft, it was cleared for further descent to 5,500 ft. This provided vertical separation with the aircraft on the Brisbane- Maroochydore track but not with PIE. About 20 seconds after clearing CZB to 5,500 ft, the controller realised that it would conflict with PIE. He instructed CZB to maintain 6,000 ft but the aircraft was already at 5,500 ft. At the time, CZB was 3.4 NM ahead of PIE. The separation standard required was 5 NM or 1,000 ft. At the time of the incident, there were 10 aircraft on the control frequency. In this high workload situation, the controller had initially forgotten about PIE. Because PIE was on another radio frequency, the option of descending that aircraft to a lower level when he became aware of the confliction was not available.