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The recent detection of the quasi-stellar object (QSO) VIKING J231818.3$-$311346 (hereafter VIK J2318$-$3113) at redshift $z=6.44$ in the Rapid ASKAP Continuum Survey (RACS) uncovered its radio-loud nature, making it one of the most distant known to date in this class. By using data from several radio surveys of the Galaxy and Mass Assembly 23$^\mathrm{h}$ field and from dedicated follow-up, we were able to constrain the radio spectrum of VIK J2318$-$3113 in the observed range $\sim$0.1--10 GHz. At high frequencies (0.888--5.5 GHz in the observed frame) the QSO presents a steep spectrum ($α_{\rm r}$=1.24, with $S_ν\propto ν^{-α_{\rm r}}$), while at lower frequencies (0.4--0.888 GHz in the observed frame) it is nearly flat. The overall spectrum can be modelled by either a curved function with a rest-frame turnover around 5 GHz, or with a smoothly varying double power law that is flat below a rest-frame break frequency of about 20 GHz and which significantly steepens above it. Based on the model adopted, we estimated that the radio jets of VIK J2318$-$3113 must be a few hundred years old, in the case of a turnover, or less than few$\times$10$^4$ years, in the case of a break in the spectrum. Having multiple observations at two frequencies (888 MHz and 5.5 GHz), we further investigated the radio variability previously reported for this source. We found that the marginally significant flux density variations are consistent with the expectations from refractive interstellar scintillation, even though relativistic effects related to the orientation of the source may still play a non-negligible role. Further radio and X-ray observations are required to conclusively discern the nature of this variation.