Are you open to day care or just a few hours playgroup?
I would think it's not necessary to put toddlers below 2-3 years old in playgroups. If you're looking for socialising, maybe you can set up playdates with other mummies at each others' homes?
Besides, day care/ playgroup can be expensive. But if you still want to try it out, I heard Bright Kids is recommended
http://www.brightkids.com.sg/branches-punggol-192
Or E-Bridge (I live very close to it)
http://www.e-bridge.edu.sg/
Kammy Mayer Zou