The Geminid meteor shower will reach its peak on December 13,14 and 15, but some of its meteors could be glimpsed between December 6 and 19. Unfortunately the big Waning Moon (Disseminating Phase, after the Full Moon on December 10) may conceal many of its shooting stars (up to 80/120 per hour! One of the best meteors showers of the year). The spectacle will be worth the effort of rising early though, especially if you live away from city lights.
The constellation of Gemini, from which this shower radiates, rises before midnight in mid-latitudes in the Southern Hemisphere, so there would be many hours of opportunity for observation. The shooting stars will appear to generate in the vicinity of Castor (with Pollux, one of the Twin stars of the constellation Gemini), situated just below the Moon for southern observers. These meteors actually originate from the Asteroid Phaeton, an unusual occurrence because most showers come instead from comets.