We already have all these "services", they're just provided by different departments and multiple levels of government.

This could totally be written up into a very typical whitepaper proposing another typical MOGing, for efficiency by reducing duplication.

And any major party could support it. Maybe not the Nats, not unless there's a stadium to be built somewhere ludicrously unpopulated. 

 I don’t think we have licensing for new parents.

Yet.. 

 Good point.

Trying to decide which big four party would be the first to introduce it.

Can't rule any out. Their processes would be very different. 

 It's usually granted to everyone automatically, to be revoked at the whim of some bureaucrat if they feel inspired.