As TeV gamma-ray astronomy progresses into the era of the Cherenkov Telescope Array (CTA), instantaneously following up on gamma-ray transients is becoming more important than ever. To this end, a worldwide network of Imaging Atmospheric Cherenkov Telescopes has been proposed. Australia is ideally suited to provide coverage of part of the Southern Hemisphere sky inaccessible to H.E.S.S. in Namibia and the upcoming CTA-South in Chile. This study assesses the sources detectable by a small, transient-focused array in Australia based on CTA telescope designs. The TeV emission of extragalactic sources (including the majority of gamma-ray transients) can suffer significant absorption by the extragalactic background light. As such, we explored the improvements possible by implementing stereoscopic and topological triggers, as well as lowered image cleaning thresholds, to access lower energies. We modelled flaring gamma-ray sources based on past measurements from the satellite-based gamma-ray telescope Fermi-LAT. We estimate that an array of four Medium-Sized Telescopes (MSTs) would detect $\sim$24 active galactic nucleus flares >5$\sigma$ per year, up to a redshift of $z\approx1.5$. Two MSTs achieved $\sim$80–90% of the detections of four MSTs. The modelled Galactic transients were detectable within the observation time of one night, 11 of the 21 modelled gamma-ray bursts were detectable, as were $\sim$10% of unidentified transients. An array of MST-class telescopes would thus be a valuable complementary telescope array for transient TeV gamma-ray astronomy.