K.N.
My daughter started on goats milk and goat dairy when she was 18 months. She was diagnosed with a cows milk protein allergy (which at 4.5 years, she has still not outgrown... Yep, her dairy needs are still met with goat butter, yogurt, cheese... I do a lot of homecooking.) She was on a milk-based toddler formula until the switch, because the milk allergy had interfered with weight gain (which we didnt know and our pedi wanted her to stay on formula until her weight increased).
However, your post confused me in that you mentioned she was on lactose free formula. Goat milk still has lactose. Being lactose intolerant and having a cows milk protein allergy are two different dietary issues. Do you know which your daughter is? Lactose intolerance refers to a life long allergy, where the person's body doesn't make the enzyme to breakdown lactose (the sugar in milk). A cows milk protein allergy, on the otherhand, is an allergic reaction to the protein in cows milk; most children outgrow it between age 3-6, although others may not until 10-12.
Lactose-free foods still have cows milk protein, while a diet free of cows milk ingredients may incorporate other dairy sources that have lactose.
I don't take a cooler of milk with me, even when she was little. She drank her 16 oz of dairy at home (She never was a good drinker of straight goat milk. Instead, I would make a simple goat yogurt & goat milk smoothie--basically diluted yogurt with milk-- for her; 8oz in the morning, 8 oz in the afternoon/evening. Nutritional guidelines are for 16 oz a day once over 12 months). While out, she would have water (she actually prefers water instead of juice). However, I do have to pack snacks and lunch items for her when were headed out, because she can't eat most menu items (for example, most bread is made with milk; that limits your restaurant choices). Feel free to message me if you have questions or need on-the-go food suggestions.