Here is a nice Canon starter kit that fits within your budget:
http://www.bhphotovideo.com/c/product/680673-REG/Canon_4462B005_Canon_EOS_Rebel_T2i.html
The 18-135mm lens is overall pretty good for the money (here is a review:
http://tinyurl.com/ygkf9zj) and would be a good single carry-around lens for your travels. It is lightweight and gives you a decent zoom range (7.5x). Paired with a T2i (aka EOS 550D) camera body, you would have a very good 18 megapixel DSLR that also happens to take beautiful 1080p and 720p HD video. I've been using the T2i since March and it is a solid camera. It isn't weather sealed but I've gotten light amounts of rain on it plenty of times and it still works fine. I've even accidentally dropped it onto rocky ground while hiking in Arches National Park, and it was still completely fine after brushing it off. It has a very good automatic mode (with auto-ISO) for when you want to quickly get a shot.
Will you be photographing wildlife in Africa? If so you may want to go with a cheaper DSLR body and do whatever it takes to get a 70-300mm lens. Even 300mm isn't enough reach sometimes, but the lenses with higher focal lengths are much more expensive. B&H has a Rebel T1i (aka Rebel 500D) camera body with an 18-55mm lens, and adding a 70-300mm lens (review:
http://tinyurl.com/cajcg) brings the cost up to $1228, still within your budget. An alternate single carry-around lens would be the Tamron 18-270mm (review:
http://tinyurl.com/y8v8dbz). You could get the camera body by itself and use this single lens to handle all of your shots, with its amazing 15x zoom range.
By the time you travel, a 32GB SD card will be very cheap, and will be a perfect size for over 1,000 RAW shots or around 4-5,000 JPEG shots. I personally avoided EyeFi due to the cost and small capacity. After the memory card, you'll need a case, UV filter(s) and a spare battery (and a monopod/tripod if you want to get high quality low light shots), and you are set.