It is well known that fasting, like other obligatory acts of worship, becomes mandatory when the person reaches the age of puberty. As regards children, we would like to stress that it is highly desirable to encourage them to fast when they reach the age of seven if they are physically capable of doing so. As for your child, she can break this fasting as she not held accountable yet. She has not reached the age of maturity yet but once she comes of age, then there will be no excuse.
Drooling or swallowing one’s saliva does not invalidate one’s fasting. It is something that you cannot control and it is not that kind of food or drink that would invalidate your fasting.
More elaboration of the issue of saliva is to be found in the following by Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, who illustrates: “There is absolutely nothing wrong in swallowing your own saliva; if such a thing had been considered as invalidating fast, then we would have learned about it from the Prophet (peace and blessings be upon him) himself, for it is such an essential matter. We believe the Prophet (peace and blessings be upon him) has communicated to the Ummah in no uncertain terms everything that we must know that is of an essential nature in our religion, especially in matters of worship.
Moreover, Allah says in the Qur’an,(Eat and drink until the white thread of dawn becomes distinct from the black thread of dawn (until the appearance of true dawn).) (Al-Baqarah 2: 187) So we are told to abstain from food and drink while fasting. As Imam IbnHazm has rightly pointed out, humankind does not consider things such as swallowing one’s saliva, rinsing the mouth or answering the call of nature as akin to eating and drinking.”
In conclusion, it is OK to swallow one’s own saliva; it does not break one’s fast. Drooling is to be treated the same as saliva that does not invalidate fasting.