YOU SAID:
I do have a cat. Do you have one?
INTO JAPANESE
私は猫を飼っています。持っていますか?
BACK INTO ENGLISH
I have a cat. do you have?
INTO JAPANESE
私は猫を飼っている。ありますか?
BACK INTO ENGLISH
I have a cat. do you have?
That didn't even make that much sense in English.