Australia has high standards of hygiene, and there are few exceptional health hazards - at least in terms of disease.
No vaccination certificates are required unless you've come from a yellow-fever zone within the past week. Standards in Australia's hospitals are also very high, and medical costs are reasonable by world standards.

The National Healthcare Scheme
Medicare, offers a reciprocal arrangement - free essential healthcare - for citizens of the UK, New Zealand, Italy, Malta, Finland, Netherlands and Sweden. This free treatment is limited to public hospitals and casualty departments (though the ambulance ride to get you there isn't covered);
At General Practitioner's(GPs) you pay up front (about $30 minimum) with two-thirds of your fee reimbursed by Medicare.

Medicare Card is available from any Medicare Centre. Anyone eligible who's staying in Australia for a while - particularly those on extended working holidays - is advised to obtain one.
Dental treatment is not included: if you are in need of dental treatment in one of the larger cities, try the dental hospital, where dental students may treat you cheaply or for free.