¿Tienes un gato o un perro?

No tengo un gato ni un perro.

Is this correct?

Si, muy bien.

One substitution: No tengo ni gato ni perro. (I have neither cat nor dog.) There is no error with what you wrote, however.

Sra

Yes, your sentence is correct! You stated that you don't have a cat or a dog. In Spanish, the word "ni" is used to express "nor" or "neither," so it effectively communicates that you don't have either of those pets. Well done!