Once you are installed and have the DP for your child, you can try to see if any school accepts to take him.
However chances are practically zero, as MOE is encouraging parents to go through the 2 sessions of AEIS ( stands for admission exercise for international students... been through it last october for my daughter who since joined P3 this January) a year.
Unfortunately you're just a few weeks too late for the S-AEIS ( that takes children mid-term in local schools) and your arrival date will coincide with the start of those kids so chances of finding a available spot are really really slim.
Best bet is probably to get him a spot either for AEIS in october either going trough the schools directly for a spot next academic year ( be aware that a lot of school have waiting list for transfers of kids already in local system, so in that case they won't take on a new student)
To pass time in the mean time, most tuition centres have programs to ensure the child is at the correct academic level to join in a local school. Those program can run as long as school hours.
MOE website on AEIS :
http://www.moe.gov.sg/education/admissi ... -exercise/