Firstly congratulations. That's great news.
There is a massive network (or networks) here for parents so you are in luck. The New Mother's support group may be something you might like to join.
http://www.nmsg-singapore.com/
They hold a monthly meet up, generate a newsletter re: activities for parents with bubs/kids including regular walks and meet-ups and monthly they organise a get together at the Tanglin Gymboree. Last month I went and there was around 15 babies (and parents) at least.
If you google words like ' parents, singapore, group' you may come up with others because I am sure there are some.
It's a great way to meet people.
Good luck!