Tap water is safe to drink.
You're only required to present proof of yellow-fever vaccination if you're arriving from one of the African or Southern American countries deemed to be at risk for yellow fever. No other vaccinations are required, although all of the standard ones are recommended.
Health insurance is recommended for all visitors, even for those from countries that have reciprocal health-care agreements with Australia. Make sure you have appropriate cover if you plan on taking on any activities deemed risky, such as skiing, rock climbing or diving.
Visitors from Belgium, Finland, Ireland, Italy, Malta, the Netherlands, New Zealand, Norway, Slovenia, Sweden and the UK have reciprocal health-care agreements with Australia and can access some free or subsidised health services through Medicare; see www.humanservices.gov.au for more details.
If you've been bitten by a snake or spider or have consumed something you think might be poisonous, contact the Victorian Poisons Information Centre for advice.