Dear A.,
There could be any number of things going on with your daughter and I would suggest having her evaluated more thoroughly. This could be something hereditary, it could have been picked up by osmosis, having other family members who vomit with anxiety. It could be something situational.
My daughter went through this at night at 10. She was fine during the day but hyperventilated at night and was certain she would vomit, insisted on having a waste basket in bed with her, just in case. Well, just prior, I had spent most of my pregnancy with my son in the hospital, critically ill. It was touch and go for me and the baby. I had him, he was fine, I got to go home. Three weeks to the day later, my mother in law passed away unexpectedly. In a span of 3 months, we had a new baby, a death, moved to a new town and had Grandpa who was elderly and suffered from severe dementia living with us. It was a lot to take in in a very short amount of time and I figured it was all just too much for her. I was very understanding, but my husband at the time was not. He told her to knock it off and quit the drama and acting like a baby. I mean, she was perfectly fine during the day, but at night it built up until she was freaking out. I spent some quiet time with her one afternoon and really had a heart to heart with her. It turned out that the way our house was situated, she was afraid Grandpa was going to die in the night in his room, closest to hers, and she wouldn't know what to do. She had heard my husband tell someone that he was going to live with us until he died. She took that to mean he was with us to die. As in, on his deathbed. I had her and the baby in our room for a while. She had her sleeping bags and blankets and after about a week, I got in her bed with her until she fell asleep. I couldn't promise her Grandpa wouldn't die, but I assured her that she was safe and not to worry so much about Grandpa, we were taking very good care of him. As the days went on and she was busy with school, piano lessons and making new friends, seeing that Grandpa was fine, her anxiety went away. Once she realized Grandpa came to LIVE with us and not to DIE with us, she didn't need her barf bucket anymore. Her fear was really real to her and I'm so glad she was able to tell me the core of it so I could help her through it.
There are fears and there are phobias so like I said, get her further evaluated and try to get to the core of it.
I wish you the best.