We construct optimal designs for estimating fetal malformation rate, prenatal death rate and an overall toxicity index in a toxicology study under a broad range of model assumptions. We use Weibull distributions to model these rates and assume that the number of implants depend on the dose level. We study properties of the optimal designs when the intra-litter correlation coefficient depends on the dose levels in different ways. Locally optimal designs are found, along with robustified versions of the designs that are less sensitive to misspecification in the initial values of the model parameters. We also report efficiencies of commonly used designs in toxicological experiments and efficiencies of the proposed optimal designs when the true rates have non-Weibull distributions. Optimal design strategies for finding multiple-objective designs in toxicology studies are outlined as well.