  The upcoming radio interferometer Square Kilometre Array (SKA) is expected to
directly detect the redshifted 21-cm signal from the neutral hydrogen present
during the Cosmic Dawn. Temperature fluctuations from X-ray heating of the
neutral intergalactic medium can dominate the fluctuations in the 21-cm signal
from this time. This heating depends on the abundance, clustering, and
properties of the X-ray sources present, which remain highly uncertain. We
present a suite of three new large-volume, 349\,Mpc a side, fully numerical
radiative transfer simulations including QSO-like sources, extending the work
previously presented in Ross et al. (2017). The results show that our QSOs have
a modest contribution to the heating budget, yet significantly impact the 21-cm
signal. Initially, the power spectrum is boosted on large scales by heating
from the biased QSO-like sources, before decreasing on all scales. Fluctuations
from images of the 21-cm signal with resolutions corresponding to SKA1-Low at
the appropriate redshifts are well above the expected noise for deep
integrations, indicating that imaging could be feasible for all the X-ray
source models considered. The most notable contribution of the QSOs is a
dramatic increase in non-Gaussianity of the signal, as measured by the skewness
and kurtosis of the 21-cm probability distribution functions. However, in the
case of late Lyman-$\alpha$ saturation, this non-Gaussianity could be
dramatically decreased particularly when heating occurs earlier. We conclude
that increased non-Gaussianity is a promising signature of rare X-ray sources
at this time, provided that Lyman-$\alpha$ saturation occurs before heating
dominates the 21-cm signal.
