Are you trying to book with Qantas points or Qatar points?Who decides when to release award seats for redemption. ?
If I am not seeing availability for Mid June, is it an indication that I have no hope of securing a seat closer towards the month of June...
If I call their privilege club team, am I wasting my time if I ask them to release an award seat ?
If it is Qantas points, you have no hope. Qatar have basically stopped releasing rewards seats to Qantas points holders. There's a tiny exception for seats a few days before flight.
If it is Qatar points, most seats have been booked, but occasionally some more are released close to the date (typically 7-14 days out).