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.
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