  Core-collapse supernovae (CCSNe) are prime candidates for gravitational-wave
detectors. The analysis of their complex waveforms can potentially provide
information on the physical processes operating during the collapse of the iron
cores of massive stars. In this work we analyze the early-bounce rapidly
rotating CCSN signals reported in the waveform catalog of Richers et al 2017,
which comprises over 1800 axisymmetric simulations extending up to about 10~ms
of post-bounce evolution. It was previously established that for a large range
of progenitors, the amplitude of the bounce signal, $\Delta h$, is proportional
to the ratio of rotational-kinetic energy to potential energy, T/|W|, and the
peak frequency, $f_{\rm peak}$, is proportional to the square root of the
central rest-mass density. In this work, we exploit these relations to suggest
that it could be possible to use such waveforms to infer protoneutron star
properties from a future gravitational wave observation, if the distance and
inclination are well known. Our approach relies on the ability to describe a
subset of the waveforms in the early post-bounce phase in a simple form
depending only on two parameters, $\Delta h$ and $f_{\rm peak}$. We use this
template to perform a Bayesian inference analysis of waveform injections in
Gaussian colored noise for a network of three gravitational wave detectors
formed by Advanced LIGO and Advanced Virgo. We show that, for a galactic event,
it is possible to recover the peak frequency and amplitude with an accuracy
better than 10% for about 80% and 60% of the signals, respectively, given known
distance and inclination angle. However, inference on waveforms from outside
the Richers catalog is not reliable, indicating a need for carefully verified
waveforms of the first 10 ms after bounce of rapidly rotating supernovae of
different progenitors with agreement between different codes.
