Check out what your medical aid does offer already, they might cover it. I'm with Momentum, pretty much just a hospital plan, but they have a very nice maternity programme that's included, and (nice surprise), they are covering all the kid's vaccinations, plus two pediatrician visits in his first year.
You can get cheap vaccinations at government hospitals

, or you can get much more expensive ones that aren't government subsidized, they are different vaccines, and the timetable differs slightly. Apparently the expensive ones don't make them as sick, which is cool, and no-one wants to wait around in government hospitals all day.
So, I go to Dischem, and pay R65 for admin fees and consultation with the sister, and they claim the extra R1500 or so straight from medical aid.
There are a lot of vaccinations to be done, so you should probably check if you're covered for it, and at that price, it'll get really expensive really quickly.