Perks should represent unique things about the character. Being childish and bratty is different from animals liking you.
I am with Atomic Postman and Alphons here. Perks should aim to be something unique and specific (but not too specific) and both "Child at Heart" and "Animal Friend" are unique and specific enough to be separate perks.
To be honest, those two perks are great for roleplay value.
Games need more perks that help give character to our characters (pun intended) and help with roleplay. Like I said at the start of this post, being childish and bratty or having animals like you are two different things, and both are great to define who your character is.
Now, if all we look at is stats and "how can I get more powerful", then these perks look pretty useless, but Fallout is a roleplaying series (even if Bethesda is intent on making it an action series) and these perks are still great for roleplay.
Also, Animal Friend has two ranks, rank one animals stop being hostile, second rank makes animal become allies. This makes it quite powerful in many situations, since it affects Nightstalkers in FNV and Yao-Guai in FO3. This effect is too powerful to be added to a one rank perk by itself, let alone still giving the benefit of the "Child at Heart". You could have "Empathy" have two ranks too, but then the second rank wouldn't really affect anything else with kids, making it feel weird.
And a last note, "Empathy" is already a perk in Fallout and Fallout 2 and doesn't do anything similar to "Child at Heart" or "Animal Friend". "Animal Friend" is also a perk in Fallout 1, so calling this perk Empathy would probably feel weird, since historically, the Empathy perk has different bonuses in the classic games.