We report an analysis of one-dimensional rod-based photonic crystal nanocavities. These cavities offer opportunities for dielectric materials which lack a matching low-refractive index substrate or are limited in under-etching possibilities to create slab-based PhC cavities. They offer high theoretical Q-values exceeding 106 for transverse magnetic polarized modes with modal volumes below 2.5(λ/n)3. For practical implementations, we propose embedding these structures in a low-refractive index polymer. An analysis of intentionally introduced variations in a rod diameter reveals which design directions should be followed in order to create cavities that are most robust for fabrication-induced variations.