Wa `alaykum as-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear questioner, thank you for your question and for your concern to be pure and perform your Prayers.
As for your question, the baby’s vomit is not impure (najis) as long as it didn’t change. Some scholars considered the baby’s vomit does cause impurity to parents clothes and the surrounding things.
Responding to your question, Dr. Muhammad Salama, PhD in Islamic Studies in English and an Associate Professor at the Faculty of Islamic Science, Al-Madinah International University, states:
If the food has not changed and has been vomited as it was eaten, then it is not najasah (ritually impure). If it has changed, then scholars have differed opinions whether it is najasah or not- though those who consider it najasah maintain that if it is little in amount, still it is pardonable.
With regard to babies, they usually vomit more than adults and it has not been reported that the Prophet commanded mothers to avoid it. Therefore, a group of scholars have considered this case pardonable also due to the hardship that mothers would suffer.
Allah Almighty knows best.