My Niece and Nephew had the same issue and are taking Lactaid ultra everyday in the AM and then regular Lactaid if they have something with dairy on it
If this is more than just a one type occurrence (if it happens almost every time she drinks the milk) - she could be allergic to milk. I had a milk allergy when I was a child and the vomiting and stomach pain were two of my main symptoms - I also had horrible headaches and leg pains.
My allergy has gotten much better, however, I still find that I have trouble if I consume too much dairy at a time - headache, dizziness, upset stomach - so I have to be careful about how much I consume. Ty[ically I cannot have a glass of milk and an ice cream in the same day or I'll feel sick.
Mine is more than a simply lactoce intolerant - I have the same problem even if I use the lactose free dairy produts.
As I said, this MAY be the problem if this happens every time your daughter drinks milk. However, if it is a one type happening, chances are something she ate/drank just didnd't settle well on her stomach or she may have a stomach virus.
I hope she feels better soon.