The spectrum of instantaneous normal mode (INM) frequencies of finite Lennard-Jones clusters is studied as a function of the extent of quantum delocalization. Configurations are sampled from the equilibrium distribution by a Fourier path integral Monte Carlo procedure. The INM spectra, average force constants and Einstein frequencies are shown to be interesting dynamical markers for the quantum delocalization-induced cluster solid-liquid transition. Comparisons are made with INM spectra of quantum and classical Lennard-Jones liquids. The methodology used here suggests a general strategy to obtain quantal analogs of various classical dynamical quantities.