VH-STO [PA31] taxied at Port Macquarie for Williamtown at 0241 hours (UTC) and made his departure call on area frequency at 0246 hours. VH-TQQ [DHC8] was enroute Sydney for Port Macquarie and passed overhead Williamtown at 0242 hours with an estimate for Port Macquarie of 0254 hours. TQQ was under the control of Williamtown military ATC and the controller did not pass this position and estimate to Sydney FS in the required time. As a result the first the Sydney FS officer and the pilot of STO knew of TQQ was when the pilot of TQQ made his passing 10,000ft call on area frequency at 0247.30 hours. The FSO immediately passed the two aircraft traffic on each other [at 0248 hours] and the Williamtown controller passed the coordination at 0249 hours, with an apology. The two captains immediately initiated vertical separation until positive passing was established. TQQ maintained 5000ft on descent and STO maintained 4000ft on climb. This separation was established at 0249 hours and the two crews attained a mutual sighting at 0250 hours. The pilots state that the two aircraft were on track and over the same location at the time of passing. Weather was cloudy with some breaks and both pilots report being in and out of cloud. TQQ did remain visual throughout the lower part of its descent but STO was in IMC most of the time. Significant Factors 1. Williamtown ATC did not coordinate the Williamtown position report for TQQ to Sydney FS in the required manner. 2. Only appropriate and timely action by the Flight Service Officer and both crews avoided a separation incident.