You can consider My Gym. They offer various classes and programs that include a good mix of activities. Heard good reviews from a few friends who have brought their children there (of various ages). They mainly liked that there are activities such as free play, group activities, and gym stations. The teachers are also approachable and attentive to the children. In my opinion, I thought it would be interesting for a one-year old since there will be development of social and motor skills involved as well. Here is the list of programs available: http://www.mygym.com.sg/Gym-Classes-Programs They have trial session available and I believed it is $50 per session.
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I don't think there is any real point in enrichment classes for a 1 yr old - it will end up being more for you than them. Form a baby group together and have them all crawl around in each other's houses.
Kindyroo at Arc, little gym at forum, Julia Gabriel at Forum, Gymboree at Tanglin.
thanks