OP, you opened a huge can of worms
The problem is that there are different niches in photography. Some are relatively cheap. Some require *very* expensive (and often cumbersome) gear to photograph well.
One of these niches is sports photography, another is wildlife photography. Both of these tend to be the most expensive gear-wise. It isn't like professional photographers like to spend money or like lugging around bulky and heavy gear. It's because that is what is required to capture "good" photos of those subjects ("good" is obviously subjective).
Take all of the comments in this thread with a grain of salt. Compuwar's idea of renting gear for the trip is quite valid, assuming you have time to learn how to use it prior to the trip. If you are really a beginner, this may not be practical.
During the day, a consumer zoom may be good enough. If you are lucky there may be animals that are comfortable enough in the presence of humans that you can get relative closeups using the long end of the zoom range on a consumer lens. With almost any camera/lens you will be able to capture the sweeping nature of the scenery you will experience on the trip.
Go into the trip with appropriate expectations. This may be such a unique experience for you that *any* photos you take will be priceless. On the other hand, if you are going into it expecting to capture a lion taking down a kill filling the frame of your photo using a $700 camera/lens, that isn't likely to happen

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In 2008 I was in Hawaii and while on a whale watch cruise took the following shots. Somewhat similar to a safari. I had a Nikon D300 and 18-200 lens. Took these photos of whales. Notice that these were all taken with a "crop" sensor camera (which I think applies to the camera/lens choices you are considering). In full frame (film) terms these were all shot at 300mm. See how there really isn't enough "zoom" in the last photo to make the subject "big" (more accurately the lens' focal length isn't long enough)? Also of note, these were shot during the day in strong light. This lens isn't "fast" enough to be able to capture these moving subjects at dawn/dusk. Both of these (need for longer reach, more "zoom" in common parlance, and need to shoot in low light) are reasons people spend crazy amounts of money on gear to shoot wildlife--it isn't just because they can (being rich professional photographers??), it's because they have to. There is no other option.
Again, just keep your expectations in perspective. I think you will have a wonderful and photographically fulfilling trip with whatever gear you end up bringing
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Really close to boat at full zoom, 200mm.
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Fairly close to boat at full zoom, 200mm.
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Still relatively close, maybe 100-200 yards away (best guess from memory). Full zoom at 200mm. Was a calf and not an adult whale, but even with a relative telephoto lens the subject starts to get pretty small.