  Nearby dwarf irregular galaxies are ideal laboratories for studying the
interstellar medium (ISM) at low metallicity, which is expected to be common
for galaxies at very high redshift being observed by the James Webb Space
Telescope. We present the first high-resolution ($\sim 0.2$~pc) hydrodynamical
simulations of an isolated low-metallicity ($0.1~Z_\odot$) dwarf galaxy coupled
with a time-dependent chemistry network and a dust evolution model where dust
is locally produced and destroyed by various processes. To accurately model
carbon monoxide (CO), we post-process the simulations with a detailed chemistry
network including the time-dependent effect of molecular hydrogen (H$_2$). Our
model successfully reproduces the observed star formation rate and CO(1-0)
luminosity ($L_{\rm CO}$). We find that dust growth in dense gas is required to
reproduce the observed $L_{\rm CO}$ as otherwise CO would be completely
photodissociated. In contrast, the H$_2$ abundance is extremely small and is
insensitive to dust growth, leading to a CO-to-H$_2$ conversion factor that is
only slightly higher than the Milky Way value despite the low metallicity. An
observationally inferred dust-to-gas ratio is thus underestimated if adopting
the metallicity-dependent CO-to-H$_2$ conversion factor. The newly-produced
dust in dense gas mixes with the ISM through supernova feedback without being
completely destroyed by sputtering, which leads to galactic outflows 20% - 50%
dustier than the ISM, providing a possible source for intergalactic dust.
