Emergency warning text and siren to be sent to every phone in Australia [July 27 at 2pm AEST]
(www.brisbanetimes.com.au)
We've had state-based similar systems before, though they have sometimes been unreliable, which is why this system is being rolled out at the federal level.
But I don't think we'll be getting something similar to your amber alerts. The article only describes two levels of alert, one for serious safety threats, and one for a warning that safety threats might be along soon.