Praise be to Allaah. 

Ibn al-Qayyim said: Saliva and spittle are things that are widespread. The Lawgiver knew that small children vomit frequently and that they cannot wash their mouths, and that their saliva will drop on those who take care of them. So the Lawgiver does not command us to wash our clothes of that or say that we are not allowed to pray in those clothes; neither are we commanded to avoid the saliva of small children. A group of the fuqaha’ said, this is a kind of impurity which is overlooked because of the essential difficulty (of avoiding it), like the mud in the streets, and impurity after istijmaar (cleaning oneself after defecating), or the impurity found on the bottom of khufoof (leather slippers) and shoes after rubbing them on the ground (to clean them)… The child’s saliva is considered to purify his mouth (after vomiting), in order to avoid hardship, just as the saliva of the cat is considered to purify its mouth. The evidence for that is the report narrated by Abu Qutaadah (may Allaah be pleased with him), who said that the Prophet (peace and blessings of Allaah be upon him) used to tilt the vessel so that the cat could drink from it, then he would do wudoo’ with the water that was left.