A Ho:YAG ceramic microchip laser pumped by a Tm fiber laser at 1910 nm is passively Q-switched by single- and multi-layer graphene, single-walled carbon nanotubes (SWCNTs), and Cr2+:ZnSe saturable absorbers (SAs). Employing SWCNTs, this laser generated an average power of 810 mW at 2090 nm with a slope efficiency of 68% and continuous wave to Q-switching conversion efficiency of 70%. The shortest pulse duration was 85 ns at a repetition rate of 165 kHz, and the pulse energy reached 4.9 μJ. The laser performance and pulse stability were superior compared to graphene SAs even for a different number of graphene layers (n=1 to 4). A model for the description of the Ho:YAG laser Q-switched by carbon nanostructures is presented. This modeling allowed us to estimate the saturation intensity for multi-layered graphene and SWCNT SAs to be 1.2±0.2 and 7±1 MW/cm2, respectively. When using Cr2+:ZnSe, the Ho:YAG microchip laser generated 11 ns/25 μJ pulses at a repetition rate of 14.8 kHz.