VH-ELZ departed Brisbane for Toowoomba and was given an initial heading of 270 degrees. Two minutes later, VH-SGQ departed, also for Toowoomba, and was given a departure heading of 240 degrees. At about the same time, Approach instructed VH-ELZ to turn on to 240 degrees. The aircraft came within 3 miles of one another without vertical separation existing. Approach was occupied by a trainee under the supervision of a training officer at the time of the occurrence. The trainee had recently transferred from another centre where Tower did not depart aircraft less than three minutes apart. This was to ensure that five miles separation existed when the aircraft contacted Approach. In this instance, the trainee was surprised when VH-SGQ departed less than three minutes after VH-ELZ. The training officer said that he misjudged the level of expertise of the trainee. This probably affected how closely he monitored the trainee, allowing the loss of separation to develop. The following factors contributed to the development of this occurrence: 1. The Approach position was occupied by a trainee controller under the supervision of a training officer. 2. The trainee expected the second aircraft to be further separated from the first than was the case. 3. The training officer misjudged the level of expertise of the trainee.