  We introduce the Australia Telescope Compact Array (ATCA) rapid-response mode
by presenting the first successful trigger on the short-duration gamma-ray
burst (GRB) 181123B. Early-time radio observations of short GRBs may provide
vital insights into the radio afterglow properties of Advanced LIGO- and
Virgo-detected gravitational wave events, which will in turn inform follow-up
strategies to search for counterparts within their large positional
uncertainties. The ATCA was on target within 12.6 hr post-burst, when the
source had risen above the horizon. While no radio afterglow was detected
during the 8.3 hr observation, we obtained force-fitted flux densities of $7
\pm 12$ and $15 \pm 11~\mu$Jy at 5.5 and 9 GHz, respectively. Afterglow
modelling of GRB 181123B showed that the addition of the ATCA force-fitted
radio flux densities to the Swift X-ray Telescope detections provided more
stringent constraints on the fraction of thermal energy in the electrons
(log$\epsilon_e = -0.75^{+0.39}_{-0.40}$ rather than log$\epsilon_e =
-1.13^{+0.82}_{-1.2}$ derived without the inclusion of the ATCA values), which
is consistent with the range of typical $\epsilon_e$ derived from GRB afterglow
modelling. This allowed us to predict that the forward shock may have peaked in
the radio band $\sim10$ days post-burst, producing detectable radio emission
$\gtrsim3-4$ days post-burst. Overall, we demonstrate the potential for
extremely rapid radio follow-up of transients and the importance of triggered
radio observations for constraining GRB blast wave properties, regardless of
whether there is a detection, via the inclusion of force-fitted radio flux
densities in afterglow modelling efforts.
