Brucellosis is a zoonotic disease caused by bacteria of the genus Brucella, posing a significant threats to human health and the development of the livestock industry. Experimental studies have demonstrated significant differences in infection rates among sheep of different ages and sexes. Based on this, this paper develops a time-delayed dynamical model for brucellosis transmission with age-sex structure, coupling the sheep population with environmental contamination, and incorporates a latency time delay to characterize the temporal delay in disease transmission. First, the basic reproduction number is calculated, and the global stability of both disease-free and endemic equilibria is established. Second, for three control measures (i.e., vaccination, isolation of infected sheep, and environmental disinfection) the target reproduction numbers are computed to quantitatively evaluate the relative effectiveness of each strategy in mitigating brucellosis transmission. Numerical simulations reveal that increasing the time delay reduces the number of infected sheep and the concentration of Brucella in the environment. When the target reproduction number exceeds 1, vaccination achieves optimal control efficacy, with required coverage decreasing as the time delay increases. In addition, by adjusting the input rates of female and male lambs and the time delay, the cost-effectiveness of age-based and sex-based vaccination strategies is compared, identifying the parameter regions where each strategy is economically dominant.