Temperature dependent extended x-ray absorption fine structure (EXAFS)spectra were measured for a 3.3 at\% Ga stabilized Pu alloy over the range $T$= 20 - 300 K. EXAFS data were acquired at both the Ga $K$-edge and the Pu$L_{\textrm{III}}$-edge. Curve-fits were performed to the first shell interactions to obtain pair-distance distribution widths, $\sigma$, as a function of temperature. The temperature dependence of $\sigma(T)$ was accurately modeled using a correlated-Debyemodel for the lattice vibrational properties, suggesting Debye-like behavior in this material. Using this formalism, we obtain pair-specific correlated-Debye temperatures, $\Theta_{\textrm{cD}}$, of 110.7$\pm$1.7 K and 202.6 $\pm$3.7 K, for the Pu-Pu and Ga-Pu pairs, respectively. The result for the Pu-$\Theta_{\textrm{cD}}$ value compares well with previous vibrational studies on $\delta$-Pu. In addition, our results represent the first unambiguous determination of Ga-specific vibrational properties in Pu-Ga alloys, i.e, $\Theta_{\textrm{cD}}$ for the Ga-Pu pair. Because the Debye temperature can be related to a measure of the lattice stiffness, these results indicate the Ga-Pu bonds are significantly stronger than the Pu-Pu bonds. This effect has important implications for lattice stabilization mechanisms in these alloys.