I would like to recommend MyGym. They have many branches in Singapore. MyGym is very fun and interactive. They integrate music and movements during the class. I would say gym class does help a little one to gain more confident over their body movement and thus helping in motor skills.
Go for a trial class or one-off promo class to let yr child try out first. Gym classes are to help them move and get familiar with their bodily movement, work those muscles and socialise a little. It might help with walking since there's "practice" but not a guaranteed.
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I am not sure about making them walk earlier, but they are great fun. I would highly recommend taking your kid to one of them. And about 8 months or when they start crawling is a good time to start.
thanks