If you catch something highly transmissible (eg, gastrointestinal illnesses) during the conference, please do not attend the conference that day and give the organisers a heads up. linux.conf.au has had major problems with outbreaks of gastrointestinal problems before.
For emergencies requiring immediate medical attention or for a crime in progress or similar (not trivial stuff), you can contact fire, police and ambulance operators as follows:
Ambulance service in Tasmania is free. Call 000.
If you find yourself in need of some medical attention while you're in Hobart there are lots of options around Sandy Bay and Hobart generally.
The Uni Doctors are located on campus in the University Union building: Phone (03) 6226 2102
If you can't get into either is a list of many other general practitioners; look for the ones in Sandy Bay and the city. http://www.gpsouth.com.au/directory_body.html Note not all GPs are interested in taking new patients.
The After Hours Doctor is an emergency clinic located at 252 Main Road, Derwent Park, not far from Hobart (about 15 minutes in a cab), open only on weeknights, weekends and public holidays. You can rock up without an appointment, but you can call them on (03) 6274 4250.