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Piccolo House is amazing!! This link also has more suggestions http://www.expatliving.sg/kids/pregnancy_childbirth/Childrens-shops-in-Singapore-Over-30-of-our-favourite-stores-and-websites-for-kids-47530.ece
Worth to go to 1km mall to take a look. Got a Japanese furniture shop there for your options! A bit ex though.
Go to UE square. They have kids furniture there. Dont know the shop name. Sorry.
I am not sure about others. But i like Ikea's. Heavy and sturdy!