Being born in the Southern Hemisphere, in Australia or elsewhere, does not change how rashi, nakshatra or lagna are calculated. It does change a couple of practical, everyday things worth knowing.
The core calculation is unaffected
Rashi and nakshatra depend on where the Moon actually is against the sidereal zodiac at your birth moment, a purely astronomical fact that does not depend on hemisphere. Lagna depends on the local sidereal time and your exact latitude and longitude, both of which the calculation already accounts for regardless of hemisphere.
What genuinely differs: seasons and sunrise timing
Sunrise, sunset, and day length in Australia run on the opposite seasonal calendar from India (Australian summer overlaps Indian winter, and vice versa). This matters for anything computed from sunrise, such as Rahu Kaal and Abhijit Muhurat, since day length itself varies more dramatically at higher southern latitudes during their winter and summer.
A note on Vaastu and directional traditions
Some directional traditions (like which direction a home entrance should face) are occasionally discussed as needing adjustment in the Southern Hemisphere, though this is a separate topic from birth chart astrology and not something rashi or nakshatra calculations are affected by.
Compute your chart
Use the kundli tool with your Australian birth city; it is calculated with the same precision as anywhere in the world.
This information is descriptive.