I also use The Kiddies' Clinic - they charge $55 or $65 for a consultation depending on which doctor you see. Also started with Dr Kumar, as he was the one recommended by my gynae, but he always seems to be very busy and I felt a bit rushed through check-ups. Also there always seems to be a long wait for him.
We now see Dr Kenny Ee, also at Kiddies' Clinic. (Other people have raved about Dr Siva.) They are all available by phone outside working hours, which we have had to use on a couple of occasions.
My only issue with Kiddies' Clinic is that they always use Mount E if the child has to be admitted to hospital, and I've not been that impressed with Mount E. Would be interested if anyone else can recommend a paediatrician that is linked to another hospital.