I don’t think that many studies have been done on that particular part as opposed to other violence.
Generally speaking, I think it’s better for a child to get a real view of the natural world - lions eat gazelles - instead of the Disneyfied one - nobody eats anything/ all are one happy family.
However, I don’t know animal planet. How detailed do they show the violence? Is it one shot of the lion killing the gazelle, and then some shots from the distance of the lions sitting at the carcass, or does the camera linger on the death pain of the gazelle and show closeup of the gory entrails?
Have you talked with your kid about that?
One difference between “violence” that animals do and violence that humans do is intent: Animals aren’t really using violence in the human sense, they are following their instinct and they need to get something to eat. So the orcas aren’t torturing the seals because they don’t follow an ethical code and don’t know other options like a quick kill. They also can’t think about other options.
Humans do have ethical codes, they are able to think about options (quick bullet to the head vs. stomach shot), and they are able to emphatize with other beings (would I want that to happen to me?). Showing violence where the hero kills mooks by the dozens without remorse therefore does indeed desensitize kids, because it shows that some people are not human beings with families, thoughts and emotions to show empathy to, but just mooks that can be killed without remorse, consideration or even stopping. Too much of that does have measurable effects.
The best advice in general about the TV watching habits is to talk with the kid (not lecture) about it: what is shown? How do you feel about it? What do you watch? How do you select good from bad shows? Do you understand what you’re watching? If not, do you want me to explain, or do you know where else you can look up information? (e.g. 8 out of 10 attempts by lions on gazelles fail and the prey gets away - but that would be boring in a documentary, so it looks as if lions are killers).
That only works if you select what shows you watch, too, of course.
It also depends on the kid - each kid is different, so what affects one very badly is less of a problem to another.
To some kids at a certain age, violent fisticuffs (like the spaghetti westerns) are so unreal that they are funny, not threatening. But the main evening news at 8 PM, showing real war and hate crimes were very disturbing when I was 10, 11 years old. So showing a lion mauling a deer might scare a kid because it’s real and not pretend, or might be shrugged off as “that’s how nature is, humans can be different”.