  (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.
