I'm not sure if you can get the prepaid SIMs at the airport - but you most certainly can get them almost anywhere else in Singapore. If you're staying at the CBD (Central Business District) or anywhere near Orchard, there're a Plethora of these available for purchase.

For starters, you could check out the 3 telcos in Singapore

Singtel - http://www.singtel.com
M1 - http://www.m1.com
Starhub - http://www.starhub.com

Enjoy your stay at Singapore