  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.
