1. What animal do you keep?

2. What pet animal do you have?
3. What pet do you keep?
4. Which pet do you have?
5. What pet do you have?
- I have a pet turtle.

(Which question is suitable for the answer?)

I'd ask this question:

What kind of pet do you have?

I have a dog, snakes and spiders.

The suitable question for the answer "I have a pet turtle" would be:

1. What animal do you keep?