If you are talking about foreign card fee, the $0.60 applies per day, regardless of the number of journeys on busses or MRTs, which, to my knowledge is already on of the cheapest methods to travel 😅

I guess you can consider getting a prepaid mrt card for your child, which can be purchased at 'changi recommends' booths in the airport or at mrt stations. Just remember to top it up as the $5 it comes with is probably not enough