  In this work, we study the properties and structure of a massive and rapidly
rotating protoneutron star (PNS) with hyperon content. We follow several stages
of quasi-stationary evolution in an approximate way at four discrete steps. We
use a density-dependent (DD) relativistic mean field theory (RMF) model and
calculate different quantities such as mass, equatorial radius, moment of
inertia, and quadrupole moment to get different rotating configurations upto
the mass-shedding limit. We study the effect of the appearance of $\Lambda$,
the lightest of all hyperons, on each of the evolutionary stages of the PNS. We
also check its sensitivity to the inclusion of $\phi$ vector meson as a
mediator of $\Lambda-\Lambda$ interaction in detail. Finally, we investigate
the universal relations between moment of inertia and compactness in the
context of a hot and young compact object.
