A person or animal that never stays in one place and is always moving can be described as a "nomad." Nomads typically migrate from one location to another in search of resources or better living conditions. In a broader sense, such individuals may also be referred to as "wanderers" or "roamers," reflecting their constant movement and exploration.
A restless person.
What is a person who steers a desert animal called
dog
A person who studies animal life is called a zoologist.
scientist
spine
The state of holding a person within a person or an animal within an animal is called pregnancy. When humans or animals are pregnant, they are literally holding a human or animal - respectively - within them.
transfering
A vegetarian.
A person who eats animal flesh is commonly referred to as an omnivore.
A lover of animals or a person opposed to animal cruelty is called a zoophile.
A person who hunts animals for their fur is called a fur trapper.