  Observations by the Atacama Large Millimetre/sub-millimetre Array of the 358
GHz continuum emission of the gravitationally lensed quasar host RX
J0911.4+0551 have been analysed. They complement earlier Plateau de Bure
Interferometer observations of the CO(7-6) emission. The good knowledge of the
lensing potential obtained from Hubble Space Telescope observations of the
quasar makes a joint analysis of the three emissions possible. It gives
evidence for the quasar source to be concentric with the continuum source
within 0.31 kpc and with the CO(7-6) source within 1.10 kpc. It also provides a
measurement of the size of the continuum source, 0.76 $\pm$ 0.04 kpc FWHM,
making RX J0911.4+0551 one of the few high redshift galaxies for which the dust
and gas components are resolved with dimensions being measured. Both are found
to be very compact, the former being smaller than the latter by a factor of
$\sim$3.4$\pm$0.4. Moreover, new measurements of the CO ladder $-$ CO(10-9) and
CO(11-10) $-$ are presented that confirm the extreme narrowness of the CO line
width (107$\pm$20 km s$^{-1}$ on average). Their mere detection implies higher
temperature and/or density than for typical quasar hosts at this redshift and
suggests a possible contribution of the central AGN to gas and dust heating.
The results are interpreted in terms of current understanding of galaxy
evolution at the peak of star formation. They suggest that RX J0911.4+0551 is a
young galaxy in an early stage of its evolution, having experienced no recent
major mergers, star formation being concentrated in its centre.
