If you are looking to enrol your children starting in January, you may also want to consider schools whose academic year starts in January. This might ease the transition for your children, as they'll be starting a new school year together with their classmates instead of coming in mid-way.
Two
International Schools with an academic school year starting in January that offer primary education are the
Australian International School and Avondale Grammar School.
You may also want to think about location. Singapore is quite small, but it can nonetheless make for quite a long commute each day if your childrens' school is far from where you are living. Do you already have a place to stay, or are you choosing a school first?
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Good luck!