Hi ,
We came out here to WA in October last year , and my wife was 18 weeks pregnant, registered with Medicare, went to local docs & got booked in for 20wk scan over here. Had regular antenatal check ups & a lot of docs/ midwives are from the uk. Hospitals are great & feel very confident about having the baby over here any day. Also we are entitled to a baby bonus of $5000 to help with initial maternity costs. When the baby is born it automatically becomes an Australian citizen and can have dual nationality.
Flight wise, airlines vary in carrying a pregnant lady. Long haul some ill let you fly as late as 36 wks but most are less & would need a doctors note. It's personal choice with flying with newborn can travel with a 2wk old but bear in mind you will not necessarily have extra seat space so could have the wee one sat on your lap the whole way here.
Best of luck, it's really daunting making the decision to have the baby in the uk or Australia, but we felt if we waited until the baby was born in the uk, we would probably miss the golden opportunity to come out here.
Good luck.