Hi MrsCravendale,
We moved to Sydney when I was 15 weeks pregnant. I'm actually Australian but had been away for 10 years so my Medicare had expired. It was extremely easy to get back onto it though - and in fact it was even easier for my English husband; he just needed to show his passport and visa (and ahve an address!) They give you a temporary / paper Medicare card until they send your 'real' one in the post.
If you ARE pregnant when you arrive, make sure you tell them when you apply for your Medicare card - they will ensure you are on the 'family safety net' which entitles you to various additional rebates.
Also, as you have residency visas you will be entitled to Medicare benefits even if you are pregnant when you get here - the 'pre-existing conditions' only applies to private health insurance.
We wanted to find somewhere to live pretty quickly as although you can register with any GP, I wanted one close to home - and I also wanted to know which hospital I'd be giving birth in! My GP has been amazing (she also bulk bills - which means that like in the UK, i don't pay anything for seeing her. If you get a GP who doesn't bulk bill (and a lot don't) you will pay a fee but then you can claim back a certain amount from Medicare).
I'm going public; as a PP said you need to have the appropriate maternity cover for at least 12 months. However, from 1 January this year the Federal Government changed the Medicare limits for private obstetric services, so whereas someone who had a baby last year, or was 20 weeks pregnant before 31 December 2009, got back 80% of their fees, now they are capped at $465 - which means you can end up being out of pocket a LOT.
If you are planning to go to Melbourne, you'll be fine in the public system anyway as the hospitals and staff in the big cities are fantastic - I'd be more concerned about going private if I was somewhere where the public hospital was a bit run down or suffering staffing shortages.
Personally, I've found the care here far superior to what I had in my first trimester in the UK - and I was in central London, with St Thomas' as my hospital! I had to chase for EVERYTHING - appointments, blood test results (which I didn't get before I left for Australia - grr) - and found that it was difficult to find out from one place what I needed to do when. Here, it all seems so much smoother. I am seeing the same midwife all the way through and in fact she will be on call for when I give birth. I'm under the care of an OB but will only see him if there's a complication... but at least I know he's there. My hospital has birthing suites, birthing pools etc, and provides great services like breastfeeding, calm birthing, etc courses. The average time people seem to stay in hospital is 3-4 days which is nicer than 24 hours I know friends have said is normal in the UK.
(A word about private health insurance. It's probably worth getting family cover while you are pregnant as that way your baby will be covered as soon as it's born. And you'll get things like dental, optical, alternative therapies and many hospital treatments covered. Importantly, you'll also get ambulance cover - which is NOT covered by Medicare. When I left 10 years ago, the average cost of a 10 minute ambulance journey was $700 so I imagine it's at least double that now. You can also take out ambulance cover on its own but with a family it makes sense to get private cover. AND, if you're under 30, or recently arrived in Australia - you need to get a 'letter of eligibility' from Medicare - you will only ever pay the premium of someone under 30, as long as you have private cover. The Government also has a 30% rebate for people who take out private cover.)
Sorry for the mammoth post! But given I am just going through it myself, I thought this info might be useful