We present a catalogue of positions and correlated flux densities of 410 flat-spectrum, compact extragalactic radio sources, previously detected in the AT20G survey. The catalogue spans the declination range [-90 deg, -40 deg] and was constructed from four 24 hour VLBI observing sessions with the Australian Long Baseline Array made at 8.3 GHz. The detection rate in these experiments is 97%. The median uncertainty of source positions is 2.6 mas, the median correlated flux density at baseline projections lengths longer than 1000 km is 0.14 Jy. The goal of this work is 1) to provide a pool of sources with positions known at the milliarcsecond level of accuracy that are needed for phase referencing observations, for geodetic VLBI, and for space navigation; 2) to extend the complete flux-limited sample of compact extragalactic sources to the southern hemisphere; and 3) to investigate parsec-scale properties of high-frequency selected sources from the AT20G survey. As a result of the campaign, the number of compact radio sources with declinations < -40 detectable with VLBI with measured correlated flux densities and positions known with the milliarcsec level of accuracies increased by a factor of 3.5. The catalogue and supporting material is available at http://astrogeo.org/lcs1 .