We use density functional theory and Monte Carlo lattice simulations to investigate the structure of ZrO2 monolayers on Si(001). Recently, we have reported on the experimental growth of amorphous ZrO2 monolayers on silicon and their ferroelectric properties, marking the achievement of the thinnest possible ferroelectric oxide [M. Dogan et al. Nano Lett., 18 (1) (2018) [1]]. Here, we first describe the rich landscape of atomic configurations of monocrystalline ZrO2 monolayers on Si and determine the local energy minima. Because of the multitude of low-energy configurations we find, we consider the coexistence of finite-sized regions of different configurations. We create a simple nearest-neighbor lattice model with parameters extracted from DFT calculations, and solve it numerically using a cluster Monte Carlo algorithm. Our results suggest that up to room temperature, the ZrO2 monolayer consists of small domains of two low-energy configurations with opposite ferroelectric polarization. This explains the observed ferroelectric behavior in the experimental films as a collection of crystalline regions, which are a few nanometers in size, being switched with the application of an external electric field.