Unfortunately long waiting lists tend to be a common problem when it comes to international schools, so I would recommend getting in touch directly with any schools you're interested in as soon as possible.
We have a comprehensive page of international schools in Singapore which lists each school's website and curriculum. You can also have a look at our write-ups on GEMS, Tanglin and ISS.
You may also find our page on Education and Schools in Singapore useful as a general overview.
Best of luck.