Constipation due to full fat cows milk

Hi guys

My daughter is 19months old and for the past 6months shes had really bad constipation to the point where she starts crying with pain. The gp have given her medication but every time she comes off it she starts having constipation again. I have a feeling that it’s due to the milk, can you please recommend an alternative milk that she can have which will help her.

Thank you ❤️❤️❤️❤️