Welcome. I will try my best to share as much info as I know.
Your Daughter would be eligible for PreK or ECE4. You should have or straight away start applying for
International School. My best advice is that you visit the websites and short list a few. You should also do a visit to really understand what each school has to offer. There are varying options on the UK system. Believe or not, although Singapore has many options, space at the bigger schools and some small goes very fast. Most of the schools will not tell you whether they have space or not and the application fees usually are not refundable. Most schools bus so you do not have to live within walking distance unless you choose. If you are moving here on an Expat package be sure that ALL school fees and multiple application fees are covered. So much about housing and school for most that take postings here is the package you are on. Consult with a relocations expert for singapore than do your own homework. There is often great debate on the forum about housing and schools, so you should weed through the postings. Please do not be put off by
some of the comments made. Singapore is lovely, There are options but I would advise you to get on to the schooling applications asap. You can choose from schools on UK, IB,Australian, American, curriculums. If you have any other queries and do hesitate to PM. Good Luck
Try to arrange for a look see asap and call schools your interested in for a tour.