I agree with hollis_f, binoculars are a must. You go to see the animals, not just to take photos.
You do not say if you have a car to yourself or have to share with strangers. this is important, because if you are with other people you cannot use a tripod in the vehicle and you may not be on the right side for a shot. In this case, a large lens will not gain you any friends in the car. Also, your driver will have to take into account the non photographers who may not want to wait for THAT shot.
I went to Kenya earlier this year, and was fortunate to have just my family and one Australian in the truck most days, but was still glad I was travelling light. I took a lightweight T3i Rebel [600D] with Canon 70-200 f4 + 1.4 converter which gave me 156-448mm reach, which was enough for 95% of shots. This was light and easy to use for 'grab' shots, of which you need plenty. [Shoot as soon as you stop, or you will end up with plenty of rear views of the skittish animals like antelope] . I also had a Fujifilm X20 around my neck at all times for when we got too close for the other camera, which sat on my lap. I took no camera bag, just wrapped them with the clothes in my hand luggage, which also brings up the point of weight. If you are using internal flights with small airstrips, the weight limit is usually 20 kilos, so bins, 2 cameras and long lens can soon add up, leaving little for clothes etc. Enjoy!