I've taken out ambulance cover with NIB on a cheap plan which also gives me dental and other perks. Medicare won't cover you for ambulance charges which can be expensive I believe so definitely find something. Yeah my main concerns are with birth related services and not being able to claim back the full amount rather than not being able to go private. Something to look into and remember once you're on a plan for a few things you have to wait 12 months in some cases before you can claim, some babies stuff will fall under that...
It took a while to settle in but we love it. It feels like home now. I thought it may be hard being away from my folks and friends, I'm very close to them. But we Skype/Facetime almost every weekend and it feels like I see them more now! It's been 9 months and they come out tomorrow for their first visit but it really does seem to have flown by. It's great out here, the summer has been terrible but still better than a British summer and Autumn is shaping up nicely here, 26 and sunny all weekend so looking forward to making the most of it.
Good luck with the move, I remember that fun time all too well haha.