  The hyperfine 21-cm transition of neutral hydrogen from the early Universe
($z>5$) is a sensitive probe of the formation and evolution of the first
luminous sources. Using the Fisher matrix formalism we explore the complex and
degenerate high-dimensional parameter space associated with the high-$z$
sources of this era and forecast quantitative constraints from a future 21-cm
power spectrum (21-cm PS) detection. This is achieved using MERAXES, a coupled
semi-analytic galaxy formation model and reionisation simulation, applied to an
$N$-body halo merger tree with a statistically complete population of all
atomically cooled galaxies out to $z\sim20$. Our mock observation assumes a
21-cm detection spanning $z \in [5, 24]$ from a 1000 h mock observation with
the forthcoming Square Kilometre Array and is calibrated with respect to
ultraviolet luminosity functions (UV LFs) at $z\in[5, 10]$, the optical depth
of CMB photons to Thompson scattering from Planck, and various constraints on
the IGM neutral fraction at $z > 5$. In this work, we focus on the X-ray
luminosity, ionising UV photon escape fraction, star formation and supernova
feedback of the first galaxies. We demonstrate that it is possible to recover 5
of the 8 parameters describing these properties with better than $50$ per cent
precision using just the 21-cm PS. By combining with UV LFs, we are able to
improve our forecast, with 5 of the 8 parameters constrained to better than 10
per cent (and all below 50 per cent).
