Question

how do animals that don't need care as babies take care of themselves

Answer 1

They'll grow up with their instincts and the natural world around them. Not all animals need parents to survive. Such as birds, they can learn to fly on their own just by jumping from a height. 

Answer 2

their instincts are what they are borned with, just like you have the instinct to blink or breath. This helps them live in the wild, untamed and free. a learned behavoir is like teaching your dog to  sit or roll over.

so the answer to your question is instincts, it keeps them alive, living in the                                             wild is all about survival.