Do pre-existing health problems get covered by Medicare?

if I have an existing health problem for example Diabetes are there any benefits available to or am I eligible for any assistance

As a NZ citizen you will be eligible for Medicare if you are moving permanently to Australia. If you are only there for a short visit then you will only be eligible for emergency hospital care under the reciprocal healthcare agreement between the two countries. You can check out how to apply for a Medicare card at www.medicareaustralia.gov.au

Existing medical problems shouldn't be any problem for you moving to Australia on Special Category Visa, unless they are specific health problems which cause a public health concern (such as TB etc..) Diabetes should not be a problem. If you have diabetes you can also register on the NDSS which entitles you to access to subsidised diabetes products such as glucometer test strips and insulin injection needles. To do this, just ask your GP about it after you've gotten your Medicare card in Australia.