The aircraft was cleared by Townsville Sector 1 to track Mackay-Capricorn-Rockhampton at 9000 feet. This clearance was coordinated with, and acknowledged by, Rockhampton Tower. The cleared route tracked through the Shoalwater Bay military training area and a number of restricted areas in this vicinity were active. The error was detected when the aircraft called Rockhampton Tower at 28 miles on the Capricorn-Rockhampton track. There was significant military air traffic transiting from Townsville to the exercise area and in the area itself. Throughout the morning, there had been frequent changes in the activity state of the various restricted areas (there were 9 notams current at the time of the incident). Consequently, the Sector 1 workload was very high. The display showing the status of the restricted areas at the Sector 1 console had been adjusted to reflect the activity states but was open to misinterpretation as to which areas were active and which were inactive. The Sector 1 controller interpreted the display as indicating that the restricted areas were inactive and cleared the aircraft via Capricorn. At the time the clearance was coordinated with Rockhampton Tower, the controller involved was distracted and did not clearly hear the cleared route. He assumed that it must have been via reporting point Murph, which would have taken the aircraft to the west of the restricted areas. The factors considered relevant to the development of this incident were: 1. The workload in Townsville Sector 1 was very high. 2. The Sector 1 display on active restricted areas was not unambiguous. 3. The Sector 1 controller misread the display and cleared the aircraft on the incorrect route. 4. Due to a distraction in Rockhampton Tower, the controller did not hear clearly the cleared route as coordinated by Townsville Sector 1. 5. The Tower Controller did not confirm the cleared route with Sector 1.