I recently drove from the UK to Gambia and we met two mad welsh girls who were travelling all the way through West Africa by Land Rover to Togo.
They were great fun and having a blast!!
I have also travelled in east Africa and loved every minute of it. I am a bloke but would definitely say GO too - people will likely treat you with lots of respect and care for the main part.
You will obviously have to be wary of the usual dangers and keep your wits about you - we all have to do that regardless of sex.
I suggest you buy or hire from library a Lonely Planet and have a thumb through that - your route will ahve to go further than Tanzania to get you to South Africa. You could travel through Malawi, Zimbabwe, Zambia, Mozambique.
There are hepas of tour companies plying this route also - I know you are keen to travel independently but an overland truck trip is still a cool way to see Africa if you ahve not been before. Typically you camp,cook and wash up etc but they are cheap, see all the must see's and you get extra security.
If you decide to go it alone you will also have a blast!
Enjoy it!
Joey 