To form questions with 'have/has got', we place 'have' or 'has' at the beginning, followed by the subject and then 'got a...' or 'got an...'. Short answers are 'Yes, I/you/we/they have' or 'No, I/you/we/they haven't' for 'have', and 'Yes, he/she/it has' or 'No, he/she/it hasn't' for 'has'.
Answer: Has Rose got a cat? Yes, she has.