The quality factor (Q), mode volume (Veff), and room-temperature lasing threshold of microdisk cavities with embedded quantum dots (QDs) are investigated. Finite element method simulations of standing wave modes within the microdisk reveal that Veff can be as small as 2(lambda/n)^3 while maintaining radiation-limited Qs in excess of 10^5. Microdisks of diameter D=2 microns are fabricated in an AlGaAs material containing a single layer of InAs QDs with peak emission at lambda = 1317 nm. For devices with Veff ~2 (lambda/n)^3, Qs as high as 1.2 x 10^5 are measured passively in the 1.4 micron band, using an optical fiber taper waveguide. Optical pumping yields laser emission in the 1.3 micron band, with room temperature, continuous-wave thresholds as low as 1 microWatt of absorbed pump power. Out-coupling of the laser emission is also shown to be significantly enhanced through the use of optical fiber tapers, with laser differential efficiency as high as xi~16% and out-coupling efficiency in excess of 28%.