In this paper, a co-design approach for event-based optimal state regulation of an uncertain linear networked control system is presented. Both the transmission intervals and the control policy are optimized by introducing a novel performance index such that the error in the control policy due to event-based transmission can be maximized. The event-triggering mechanism uses the worst case control input error as threshold to decide the optimal transmission instants. Stochastic Q-learning approach is used to design both the control policy and event-triggering condition without explicit knowledge of the system dynamics. The event-based Q-function parameters are updated using a hybrid scheme both at triggering instants and during inter-event times to accelerate the parameter convergence. The asymptotic stability in the mean square of the closed-loop system is demonstrated using Lyapunov analysis with the assumptions of persistence of excitation of regression vector. Finally, numerical results are included to substantiate the analytical design.