Okay. First, your soon to be 12 month old does NOT need occupational therapy. None of my daughters held their own sippy cup at 12 months. My youngest is 13+ months and she is starting to hold her own sippy cup, but still hasn't figured out how to tip her head back far enough to drink from it if it is not completely full. I am not worried. Why? Because she will eventually get it as she uses it more.
My two older daughters eventually figured it out in their own time and now at 2 and 4 are pros with sippies, use straws, and drink from regular cups. I could not tell you at what age they finally figured out sippy cups, but I can say it was when they figured out they wouldn't fall backwards when they tipped their heads back when sitting. Then when they got better balance while standing and walking they figured out they would not fall drinking from sippy cups and tilting their heads.
Each child is different. Let your daughter play with the sippy cup and get used to the weight of it when there is milk in it. I started out with the sippies with handles. That seems to help. I also use sippies that are smaller around without handles so that their little hands can reach around them comfortably. Get a couple of designs and see what works best for your daughter...and give her time. She will figure it out eventually!