The Qantas spokesperson implies that it's not possible to see a passport number and DOB:
“The issue was isolated to the Qantas app with some frequent flyers able to see the travel information of other customers, including name, upcoming flight details, points balance and status. No further personal or financial information was shared and customers would not have been able to transfer or use the Qantas Points of other frequent flyers. We’re not aware of any customers travelling with incorrect boarding passes.”
However, perhaps they're just using a very carefully crafted phrase by saying "travel information... Including...(i.e. not giving an exhaustive list of shared information)", then saying "No further personal information.. was shared".
Note: Post edited for clarity