Hi Jmaz,
Our paediatrician charges R950 per visit, on average they schedule visits for 6 weeks after baby is born, at 12 weeks, 6 months and a year. Thereafter annually for a check-up. And of course you will go if baby is sick.
Whether you actually go to all the appointments that they recommend is up to you, the 6-week and 12-week one is really important because the baby is still so small then. The 6-month and 12-month one is optional in my mind, unless your baby is ill, or has a medical issue that needs constant monitoring.
As for going to the paed when baby is ill (for instance, with a bad cough), that's also up to you. I'd go if baby is still under 6 months, thereafter a decent GP is probably good enough. I'd also go if the baby appears to be sick with something other than a common cold or cough.