toddler question

my daughter is 2 years old. she barely eats any food and no meat at all what so ever. but she drinks lots and lots of 2% milk like half a gallon a day maybe a little more. she doesn't even want juice any more she drinks water sometimes. but my mom said that too much milk could harm her white blood cells... and now I'm super worried. her doc said as long as she's drinking and gaining weight (which she is) then she should be fine. but now I'm worried because of what my mom said. does any one else know if too much milk will hurt my baby? im really worried now.