All the above suggestions are good. However, from Sydney, the only direct flights to Africa are SAA and Quantas to Johannesburg.
South Africa is great and wonderful but the security situation in and near most big cities, including Cape Town, is still of concern. Out in the rural areas its not so bad.
From Johannesburg, you can fly direct to Botswana and Namibia both or which have great wildlife travel products. In Botswana, one has the Okovango and Chobe Parks. Namibia has Etosha. The only problem is that the distances are great (like the Outback!)
One country not yet mentioned and which can be reached via Jo'burg is Zambia. However, I understand these days visas are required for entry for UK,US and Aus citizens.
Tanzania is an interesting idea and one I supprt, The country has made remarkable strides in recent years. Although again distances are great, the country includes great destinations such Kilimanjaro, the Serengeti, Zanzibar, the beach coast north of Dar and if you are really being adventurous Lake Tanganyika.