Cocococo
Although I live in England, Cape Town is my home town. I could go on for days about what's good to do etc, don't worry I wont though.
Anyway good places to stay are:
The Bay Hotel (Camps Bay, near Cape Town city centre)
The Table Bay Hotel (The V&A Waterfront)
The Mount Nelson Hotel (Upper Cape Town City Centre)
These are all wonderful hotels but they are very pricey, there are loads of other really good hotels which are a lot cheaper, you should be able to see some in the websites (see url's below).
Things to see and places to go:
Take a trip up Table Mountain at sunset. You can pre-book tickets (ask your hotel or go to Vaughan Johnsons Wine Shop in the Waterfront) which include a meal & drink voucher for about £13 per person. This is a wonderfully romantic thing to do. The views are absolutely spectacular.
Kirstenbosch Botanical Gardens. Again, ask your hotel for directions. The gardens are an amazing collection of local fauna and flora, a great place for kids to run around in and they have a really nice restaurant too.
The Wine Route in Stellenbosch. For really good wine try Hartenburg Estate, they do a wonderful picnic lunch for about £3.50 per person which includes a half bottle of wine each!! There are loads of wonderful farms, you can get a map of the Stellenbosch or Paarl Wine Route and do it yourself (if you are hiring a car). Avoid Spier, it is a tourist trap and very expensive with mediocre wine.
I could go on and on about where to visit, but your best bet is to look at the following websites:
www.capetourism.org/
www.cape-town.org/
As far as travelling with a one year old goes....
If you are hiring a car, prebook the carseat well in advance. Car hire firms normally only have one or two carseats and they get booked up well in advance.
There are a lot of attractions in Cape Town which would suit a backpack/child carrier, if I was going as a tourist I would definitely invest in one.
Don't worry about nappies, food or any baby products (you may want to take your own formula if still using it). Get somebody to point out your local supermarket, these items are readily available.
You can drink the tap water.
When travelling from Cape Town International Airport, give yourself plenty of time for check-in. They often give preference to those with children but that is not a hard and fast rule. We always aim to be at the airport at least 3 hours prior to departure.
Hope this helps
Have a GREAT holiday in beautiful sunny Cape Town