Can you say "raise an animal"?

It was said as a way to comfort someone who had just broken up with her boyfriend, and someone said something like "go raise a dog".

I know it's okay to say raise an animal; I just feel so weird about it. Don't we normally say raise a child? I mean, in my opinion, isn't raise only used for human beings?

For animals, like pets, which verb is more appropriate to use? Do we just use raise all the time, no matter if referring to people or animals?

While raise is used for animals, it is usually in an agricultural setting. You are right to think it sounds unusual to speak of raising a household pet such as a dog or cat. It is much more common for someone to say that they have or that they own a dog. If one raises an animal, or animals, it is almost always for a specific purpose (other than companionship) such as meat production or breeding.

What this says about our use of raise for children, I'm not quite sure.

The New Oxford American Dictionary (in OS X) says of raise:

bring up (a child) : he was born and raised in San Francisco.

breed or grow (animals or plants) : they raised pigs and kept a pony.

The word rear might seem less weird to you:

(usu. be reared) bring up and care for (a child) until they are fully grown, esp. in a particular manner or place : he was born and reared in New York City | a generation reared on video.

breed and raise (animals) : the calves are reared for beef.

It can be used for animals, and plants.

They raised pigs and kept a pony.

When referring to an animal, or a plant, raise means "breed or grow."

I was taught that you raise a pig and you rear a child in English class, but no one cares or knows the difference today…just use raised for either one.