We investigate the quantum optical properties of a quantum-dot dipole emitter coupled to a finite-size metal nanoparticle using a photon Green-function technique that rigorously quantizes the electromagnetic fields. We first obtain pronounced Purcell factors and photonic Lamb shifts for both a 7- and 20-nm-radius metal nanoparticle, without adopting a dipole approximation. We then consider a quantum-dot photon emitter positioned sufficiently near the metal nanoparticle so that the strong-coupling regime is possible. Accounting for nondipole interactions, quenching, and photon transport from the dot to the detector, we demonstrate that the strong-coupling regime should be observable in the far-field spontaneous emission spectrum, even at room temperature. The vacuum-induced emission spectra show that the usual vacuum Rabi doublet becomes a rich spectral triplet or quartet with two of the four peaks anticrossing, which survives in spite of significant nonradiative decays. We discuss the emitted light spectrum and the effects of quenching for two different dipole polarizations.