All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
According to the Fatwa of the majority of the Muslim scholars, impure vomit is that which comes out of one`s stomach after having settled in it, as clarified in the Shafie book {Moghni Al-Mohtajj, vol.1/pp.232}. However, milk coming directly from a baby`s mouth before reaching its stomach isn`t considered vomit, and remains pure because things are, in principle, pure. And Allah Knows Best.