Follow up to this post, as my trip approaches...
The tour company sent me a packet with more info. We will be doing some touring in Range Rovers, but will also be walking a few miles a day over uneven terrain. We will sometimes be traveling in small planes, so there are strict weight limits. 44 lbs. for the provided duffel bag, and 15 lbs. for the carry-on. I plan to put all my camera gear in the carry-on.
They said point and shoot cameras don't have enough range for wildlife. They recommend a superzoom camera, or a DSLR with a mid-range zoom (up to 300mm) and a fast prime for low-light shooting.
Based on the comments in this thread, I am going to try to bring two bodies. Both so I have a backup, and so I don't have to switch lenses in the field. I have a 5D Mark II. I was going to convert it to IR, but I think I'll hold off until after the trip. I plan to buy a 5D Mark III, and will bring that, too. Electricity will be unreliable, so they recommend bringing extra batteries.
I'm still deciding on lenses. The lens I bring when I bring only one lens is the 24-105. But I'm thinking I might want to go longer and wider. Maybe my 16-35mm F/2.8 instead of a fast prime, and my 70-200 f/4 plus 1.4 extender. Not as fast as the f/2.8, but so much lighter.
I usually use prime lenses when I need reach, so the 70-200 the longest zoom I have. Well, I have a Sigma 150-500mm, but it's too bulky for this trip. I am considering buying a zoom lens for the trip.
I think the 28-300mm will be too heavy. The 70-300mm and the 100-400mm are possibilities. The 100-400mm might also be too heavy, though it has the advantage of being compatible with the Canon extenders.
I am planning to buy the Pocket Rocket card holders as Vivid Color recommended, and the B&W filters (once I nail down what lenses I'm bringing). And I'm stocking up on memory cards.
Still considering what other cameras I'll bring. I have a point and shoot Lumix I use as a backup and when I don't want to bring all my gear. (I'm planning to leave my smartphone at home.) And a SX50 HS. The superzoom might come in handy, though I am generally not thrilled with the image quality. I also have a point and shoot Lumix that's been converted to infrared. I love IR photography, but I doubt I'll have time on this trip for the long exposures needed when using an IR filter on a regular camera.
Having done the safari this time last year (Botswana/Zambia), my advice is to remember to enjoy the moment, not just the photography. You can go to a Zoo to photograph animals up close, but it's being with them in the wild that makes it so special. Breath it in. Post some pics when you get back.