You can check out this website for suggestions of Holi events happening in Singapore this year. http://www.ibtimes.sg/holi-2016-top-places-celebrate-festival-colours-singapore-708 But from what I've observed, alot of these events mention admission for "children 4 and above". These events might not be too conducive for babies, with the music, dancing, crowds and while some of the events state that the coloured powder used in the festival is safe and non-toxic, it is unclear if it will still be safe for baby.
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Let's Play Holi A cultural family event with loads of Bollywood beats by DJ Milan, accompanied by the Singapore Dhol Federation with their percussive beats. Venue : Esplanade Lawn Date - 26th March Ticket : Free
Sentosa usually has something every year