Adequately balanced daily food rations that provide the body with sufficient amounts of energy and nutrients, including minerals, are particularly important in early childhood when rapid physical, intellectual and motor development takes place. Cow’s milk (CM) and young-child formulas (YCFs) are introduced to a child’s diet past the first year of age. The main aim of the present study was to perform a qualitative and a quantitative analysis of daily food rations of young children based on the recommendations of the daily food ration model. An attempt was also made to determine whether the type of consumed milk (YCF or CM) adequately meets young children’s energy demands and contributes to the incorporation of different food groups into a balanced and healthy diet for children aged 13–24 months. A total of 714 parents between October 2019 and March 2020 filled out a food frequency questionnaire. In the second stage of the study, the parents participated in a dietary recall and were asked to keep diaries of all meals and foods consumed by children over a period of three days. The mean daily intake of CM/YCF and fermented milks was determined at 360 mL ± 128 mL, and it accounted for 55.4% of the guideline values. Flavored dairy products were consumed more frequently than fermented milks without added sugar or flavoring (94 ± 17 g vs. 56 ± 26 g, p < 0.05). Diets incorporating CM were significantly more abundant in protein than YCF diets (29.3 g vs. 21.9 g; p < 0.01). Liquid intake was somewhat higher in children fed YCFs (1280.8 mL vs. 1120.1; p < 0.05), mainly due to the higher consumption of fruit juice, nectars and sweetened hot beverages (246 ± 35 mL in the YCF group vs. 201 ± 56 mL in the CM group; p < 0.05). Children fed YCF consumed significantly larger amounts of sweetened beverages such as tea sweetened with sugar or honey, sweetened hot chocolate or instant teas (OR = 2.54; Cl: 1.32–3.26; p < 0.001), than children receiving CM. This group was also characterized by higher consumption of sweetened dairy products, mainly cream cheese desserts, fruit yogurt and yogurt with cereal (OR = 1.87; Cl: 1.36–2.54; p < 0.01), as well as a lower daily intake of plain fermented milks (OR = 0.56; Cl: 0.21–0.79; p < 0.001). The daily food intake and the quality of the diets administered to children aged 13–24 months were evaluated and compared with the model food ration. It was found that milk type influenced children’s eating habits and preference for sweet-tasting foods. The study also demonstrated that Polish parents and caregivers only have limited knowledge of nutritional guidelines for toddlers.