Strongly concentrated optical fields around a metal nanoparticle in the close vicinity of a dipole noticeably facilitate dramatic changes in the localized density of states due to hybrid photonic-plasmonic mode couplings as compared to that of the pure cavity mode fields. Significant variations of the field intensity in the presence of the metal nanoparticle elucidate enhanced light-matter interaction in a hybrid structure. The enhancement factor of the light-matter interaction is studied through the single-atom cooperativity parameter, which is directly proportional to the ratio of the fluorescence lifetimes of the off-resonant and on-resonant emission. A compact and cost-effective hybrid device, which includes a microfiber cavity, supporting whispering gallery modes, and a well-defined solid nanostructure, consisting of a gold nanoparticle core, overcoated by a silica shell, and decorated with CdS/CdSe quantum dots, is demonstrated to offer an outstanding potential for the enhancement of light-matter interaction. Surface plasmons of a gold nanoparticle, placed inside a hollow cylindrical nanostructure at the surface of a microfiber, are activated upon excitation of the dipoles of the quantum emitters, which are on-resonance with the whispering gallery mode. Time-resolved experiments demonstrate that the single-atom cooperativity parameter of the quantum dots is enhanced by a factor of about 4.8 in the presence of the gold nanoparticle being simultaneously in strong interaction with the cavity mode field and the metal nanoparticle's surface plasmons.