  We study the number of short geodesics and small eigenvalues on
Weil-Petersson random genus zero hyperbolic surfaces with $n$ cusps in the
regime $n\to\infty$. Inspired by work of Mirzakhani and Petri \cite{Mi.Pe19},
we show that the random multi-set of lengths of closed geodesics converges,
after a suitable rescaling, to a Poisson point process with explicit intensity.
As a consequence, we show that the Weil-Petersson probability that a hyperbolic
punctured sphere with $n$ cusps has at least $k=o(n)$ arbitrarily small
eigenvalues tends to $1$ as $n\to\infty$.
