According to Hanafis, there is no Zakaat on a non baaligh child. Zakaat is accountable on a baaligh child as from his baaligh date. But Zakaat is still not due on him. If a child became baaligh with an asset equal to nisaab or more than that, then he is accounted for Zakaat for next year. Next year, same date as when he became baaligh, if he has nisaab or more than that on his assets minus liabilities, then Zakaat is due on the remaining balance(as at that date).
Since most of us have forgotten the first date that we had nisaab after boulough, that is why we select the 1st Ramadhaan as the most ideal date of the year for Zakaat calculation.
Hanafis stipulate that there is NO ZAKAAT on non baaligh children`s assets because their wealth is a trust between our hands and imposing anything will cause detrimental to their wealth:
وَلَا تَقْرَبُوا مَالَ الْيَتِيمِ إِلَّا بِالَّتِي هِيَ أَحْسَنُ حَتَّى يَبْلُغَ أَشُدَّهُ
‘‘Do not approach the property of the orphan, except with the best possible conduct, until he reaches maturity’’(6:152) Also the beloved prophet SAW said that the child is not accounted until he becomes baaligh.(Abu Dawood)
عَنْ عَلِيٍّ عَلَيْهِ السَّلَام عَنْ النَّبِيِّ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ قَالَ رُفِعَ الْقَلَمُ عَنْ ثَلَاثَةٍ عَنْ النَّائِمِ حَتَّى يَسْتَيْقِظَ وَعَنْ الصَّبِيِّ حَتَّى يَحْتَلِمَ وَعَنْ الْمَجْنُونِ حَتَّى يَعْقِلَ سنن أبي داود
Boulough is the first ejaculation of a boy or the first mense of a girl. A girl has a minimum of nine years and a boy a minimum 12 years(Shami). That is blood flowing before ninth year of a girl are not menses. Both are baaligh in any case when they have reached 15 years. On boulough, all ahkam and impositions of Shariah are applicable including salaahs and fasting.
Worth noting that Imaam Shafi`ee holds the view that a rich child should be accounted for Zakaat even before his boulough.