Using focused ion beam etching techniques, micropillar cavities were fabricated from a high reflective AlAs/AlGaAs distributed Bragg reflector planar cavity containing self-assembled InP quantum dots in (Al(0.20)Ga(0.80))(0.51)In(0.49)P barrier layers. The mode spectra of pillars with different diameters were investigated using micro-photoluminescence, showing excellent agreement with theory. Quality factors of the pillar cavities up to 3650 were observed. Furthermore, for a microcavity pillar with 1.26 mum diameter, single-photon emission is demonstrated by performing photon correlation measurements under pulsed excitation.