(abridged) Our aim is to determine the radial abundance profile of SiO and HCN throughout the stellar outflow of R Dor, an oxygen-rich AGB star with a low mass-loss rate. We have analysed molecular transitions of CO, SiO, and HCN measured with the APEX telescope and all three instruments on the Herschel Space Observatory, together with literature data. Photometric data and the infrared spectrum measured by ISO-SWS were used to constrain the dust component of the outflow. Using both continuum and line radiative transfer methods, a physical envelope model of both gas and dust was established. We have performed an analysis of the SiO and HCN molecular transitions in order to calculate their abundances. We have obtained an envelope model that describes the dust and the gas in the outflow, and determined the abundance of SiO and HCN throughout the region of the outflow probed by our molecular data. For SiO, we find that the initial abundance lies between $5.5 times 10^{-5}$ and $6.0 times 10^{-5}$ w.r.t. H$_2$. The abundance profile is constant up to $60 pm 10 R_*$, after which it declines following a Gaussian profile with an $e$-folding radius of $3.5 pm 0.5 times 10^{13}$ cm. For HCN, we find an initial abundance of $5.0 times 10^{-7}$ w.r.t. H$_2$. The Gaussian profile that describes the decline starts at the stellar surface and has an $e$-folding radius $r_e$ of $1.85 pm 0.05 times 10^{15}$ cm. We cannot to unambiguously identify the mechanism by which SiO is destroyed at $60 pm 10 R_*$. The initial abundances found are larger than previously determined (except for one previous study on SiO), which might be due to the inclusion of higher-$J$ transitions. The difference in abundance for SiO and HCN compared to high mass-loss rate Mira star IK Tau might be due to different pulsation characteristics of the central star and/or a difference in dust condensation physics.
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