VH-AJJ departed from Telfer at time 1828 and was estimating Savoy at 1857. The pilot had planned to climb the aircraft to 39,000 feet (FL390). VH-JJQ was en route between reporting point T84B (passing it at 1757) and T84C (estimating it at 1838) and was maintaining FL270. T84C is approximately 70NM south of Telfer. The pilot of VH-AJJ called the Perth Sector 1 controller on both taxi and departure. The pilot was told to standby for an airways clearance. VH-JJQ and SIA7220, transiting on route A585 and maintaining FL330, were possible conflicting traffic for VH-AJJ. At time 1831, 3 minutes after departure, a clearance was issued to the pilot of VH-AJJ to track via Savoy and planned route with a climb to FL310. No separation standard, ie 10 minutes or 1000 feet in altitude, was established between VH-AJJ and VH-JJQ. At time 1839, VH-JJQ reported passing T84C at 1839, FL270, estimating Curtin at 1934. This transmission was made on the Perth Sector 2 (134.5) frequency. At time 1843.5, the pilot of VH-AJJ reported maintaining FL310 and requested a higher level. VH-AJJ was now vertically separated from VH-JJQ. The Controller was preoccupied with a separation problem in the vicinity of Karratha and did not fully assess the situation between VH-JJQ and VH-AJJ. It was also moderately busy at the time and a number of transmissions took place around the time of the incident. As a consequence of the workload, the Controller took the advice of the Sector 2 Controller who advised her to assign VH-AJJ FL310 due to SIA7220. The Sector 2 Controller also entered a time when VH-AJJ would leave lateral conflict with SIA7220 on the flight progress strip for the Sector 1 Controller. This led the Sector 1 Controller to think that the Sector 2 Controller had looked at the entire scenario and offered a solution that would separate all the conflicting traffic. The Sector 1 controller then issued a clearance to the pilot of VH-AJJ to climb through the level of VH-JJQ without fully assessing the traffic situation.