  We present the first of two papers dedicated to verifying the Australian
Epoch of Reionisation pipeline (AusEoRPipe) through simulation. The AusEoRPipe
aims to disentangle 21-cm radiation emitted by gas surrounding the very first
stars from contaminating foreground astrophysical sources, and has been in
development for close to a decade. In this paper, we build an accurate 21-cm
sky model that can be used by the WODEN simulation software to create
visibilities containing a predictable 21-cm signal. We verify that the power
spectrum estimator CHIPS can recover this signal in the absence of foregrounds.
We also investigate how measurements in Fourier-space are correlated, and how
their gridded density affects the power spectrum. We measure and fit for this
effect using Gaussian-noise simulations of the MWA phase I layout. We find a
gridding density correction factor of 2.651 appropriate for integrations equal
to or greater than 30 minutes of data, which contain observations with multiple
primary beam pointings and LSTs. Paper II of this series will use the results
of this paper to test the AusEoRPipe in the presence of foregrounds and
instrumental effects.
