It is recommended for nausea of any type that you don't drink fluids when eating solids. Your daughter has discovered that naturally. Because she is drinking water, you do not need to worry about dehydration. Her solids will provide her with the energy and nutrition that she needs to get through the morning. Nutrition is something to be viewed not one meal at a time, but rather as a full day or even several days to be judged for adequacy.
People can eat loads of fruits and vegetables one day, few or none the next, and still be fine.
It makes no difference if your daughter drinks her milk in the middle of the afternoon, or before bed, just so long as she gets the amount she needs. Her body will get the benefits from it no matter when she drinks it. What is important, is that you offer only healthy foods and that you are sure to allow your daughter to stay in tune to her own body. By acknowledging her early morning dislike of fluids, you are allowing her to do this. It may be that one day she will outgrow it.