A lot of parrots have weaker anchors on their tail feathers that make them fall out more easily than feathers on other parts of the body. It's believed this happens to trick and escape predators, just like how some lizards drop their tails. In budgies it takes about 8 weeks for a tail feather to regrow completely, so I'd expect about the same amount of time for a mulga parrot. If the feather was just damaged or clipped, it would take until the next molt for it to regrow, which could be at any time.