“Does milk improve immunity?”

Cow's milk will not have an impact on your child's immunity in a positive or negative way. Drinking cow's milk is not a necessity for any human being and as long as your child consumes variety of foods that provide him or her with protein, fat and calcium they will be just fine. Yogurt is another dairy food that is healthy because it is rich in probiotics - just avoid the ones with too much sugar.

From an immunity persoective, I cannot see a reason why NOT drinking milk should be a problem. From a nutrition aspect, it may decrease intake of calcium and energy intake in the form of fats and proteins.
Also, there may be a reason why your child does not like milk - lactose intolerance (unlikely) or simply taste or texture. You can discuss it with the pediatrician

Recent studies found that milk alternatives might not give kids enough vitamin D when they replace dairy milk. High quality cheese could help you, but don't forget to balance the diet with vitamins, which are contained in other products (meat, vegetables, fish, fruits, etc.)
For more information, please, take a look here:
https://milklife.com/articles/nutrition/dairy-milk-vs-almond-milk-and-milk-alternatives