  We use high-angular-resolution images obtained with SPHERE/ZIMPOL to study
the photosphere, the warm molecular layer, and the inner wind of the close-by
oxygen-rich AGB star R Doradus. We present observations in filters V,
cntH$\alpha$, and cnt820 and investigate the surface brightness distribution of
the star and of the polarised light produced in the inner envelope. Thanks to
second-epoch observations in cntH$\alpha$, we are able to see variability on
the stellar photosphere. We find that in the first epoch the surface brightness
of R Dor is asymmetric in V and cntH$\alpha$, the filters where molecular
opacity is stronger, while in cnt820 the surface brightness is closer to being
axisymmetric. The second-epoch observations in cntH$\alpha$ show that the
morphology of R Dor changes completely in a timespan of 48 days to a more
axisymmetric and compact configuration. The polarised intensity is asymmetric
in all epochs and varies by between a factor of 2.3 and 3.7 with azimuth for
the different images. We fit the radial profile of the polarised intensity
using a spherically symmetric model and a parametric description of the dust
density profile, $\rho(r)=\rho_\circ r^{-n}$. On average, we find exponents of
$- 4.5 \pm 0.5$ that correspond to a much steeper density profile than that of
a wind expanding at constant velocity. The dust densities we derive imply an
upper limit for the dust-to-gas ratio of $\sim 2\times10^{-4}$ at 5.0
$R_\star$. Given the uncertainties in observations and models, this value is
consistent with the minimum values required by wind-driving models for the
onset of a wind, of $\sim 3.3\times10^{-4}$. However, if the steep density
profile we find extends to larger distances from the star, the dust-to-gas
ratio will quickly become too small for the wind of R Dor to be driven by the
grains that produce the scattered light.
