The 69-year-old male pilot had taken the three passengers on a joy ride, police said. The plane went down into a wetland area northeast of Brisbane shortly after taking off, Reuters reported.
Pictures showed the Rockwell International aircraft floating upside down in Moreton Bay.
Police are still working to identify the male passenger and the children, whom inspector Craig White said were "younger than teenagers".
"This is a tragic accident ... In the lead-up to Christmas and the last thing that any family need to go through at this time of the year, at any time," White told reporters.
Australian Transportation Safety Board Commissioner Angus Mitchell said a report into the likely cause of the crash would be completed in six to eight weeks.