I think if you want to do walks, organise it through a guide. Even in cape Town, I would not recommend walking on Table Mountain except on the main paths without a guide. Having said that, there are lots of options and lots of lovely walks you could do in cape town and the surrounding areas. Simple walks like along the beaches (Muizenberg has a lovely long walk you can do for miles) or as you head up the coast.
South Africa with a baby is fine. If the baby is weaning, take a portable high chair as I always find that while restaurants are very friendly to children, high chairs seem to be in short supply. The garden route is lovely, but don't do it unless your baby is happy to travel in the car. Even taking a leisurely drive, you're looking at a few hours a day.
Personally, I'd go to Cape Town and just stay there for a couple of weeks. You can move around and do a lot while your'e there including walks, beaches, countryside, tourist stuff etc. It's also a major city so convenient with a baby in terms of lots of places to go and services easily available.
When travelling with a child to SA you need the child's full birth certificate. If travelling with just one parent you also need permission from the other to take the child into and out of South Africa. Bear that in mind and make sure you have the correct documentation. It will be checked.