Do note the current processing time for a new carer application is expected to be 7 years. For this reason, if applying, I recommend making an onshore application which will allow you to remain in Australia during this process time. Generally, if applying for a carer visa onshore, and remaining in Australia on a bridging visa following a visitor visa to enter Australia, you would not be eligible for medicare coverage in Australia until the carer visa is granted (except for where some foreign citizens have reciprocal health care agreements with Australia, this includes Belgium, Finland, Italy, Malta, Netherlands, NZ, Norway, Ireland, Slovenia, Sweden and the UK). However in the case you've mentioned, you would not be eligible to apply for a carer visa. The carer was must be a relative of the sponsor and this covers close relatives and extends to a grandparent, grandchild, niece/nephew or aunt/uncle. It does not include a cousin on the sponsor unfortunately.
