(1) Background: The effect of fathers on dietary intake in preschool-aged children is under-explored. The aims were to: (i) evaluate the efficacy of a family-based lifestyle intervention, Healthy Youngsters, Healthy Dads, on change in dietary intake in fathers and their preschool-aged children post-intervention (10 weeks) and at 9 months follow-up compared to a waitlist control group and (ii) investigate associations in father–child dietary intakes. (2) Methods: Linear mixed models estimated group-by-time effects for all dietary outcomes, measured by food frequency questionnaires. Cohen’s d determined effect sizes, while correlation tests determined associations in father–child dietary intakes. (3) Results: For children, medium group-by-time effects sizes were identified at 10 weeks for sodium intake (d = 0.38) and percentage energy from core foods (d = 0.43), energy-dense, nutrient-poor (EDNP) foods (d = 0.43) and prepacked snacks (d = 0.45). These findings were sustained at 9 months follow-up. For fathers, medium to large, group-by-time effect sizes were identified at 10 weeks for energy intake (d = 0.55), sodium intake (d = 0.64) and percentage energy from core foods (d = 0.49), EDNP foods (d = 0.49), and confectionary (d = 0.36). For all of these dietary variables, except sodium, effects were sustained at 9 months. Moderate to strong associations existed in father–child dietary intakes for some of the dietary variables. (4) Conclusions: Although further research is required, this study provides preliminary support for targeting fathers as agents of change to improve dietary intakes in their preschool-aged children.