This article investigates the robust output regulation of linear uncertain singularly perturbed systems by output-feedback control. Due to the presence of extremely small perturbation parameters, numerical issues will arise when applying conventional robust regulator design techniques to the regular system. To handle the problem, a continuous-time output-feedback controller adopting the forwarding design technique is proposed by combining the internal model approach with singularly perturbed theory. In this manner, the circumvention of numerical issues and the resolution of robustness problems can be achieved. Additionally, the sampling of the transmissions between the plant and the controller is taken into account, leading to the proposed implementation of a dynamic output-based event-triggered strategy. As a result, the output regulation property becomes practical. To avoid Zeno behavior, the implementation ensures the existence of a strictly positive minimum intertime for the triggering instant sequence. The validity of the results is demonstrated through the presentation of a numerical example.