How to deal with a false reports from an apartment neighbor?

My fiance and I recently moved into a new apartment. We reside on the second floor with our dog and cat. Our dog is about 40 pounds and within the regulation weight set by the apartment complex. We are both professional, quiet people. We don't own a television, and we don't listen to music. We go to bed at ten and wake up at seven. Our dog is always kenneled at night and never barks. We just received a letter from the apartment complex saying our downstairs neighbor has lodged a noise complaint with us. She is a student, and even by the apartment manager's description, rude and demanding. The girl complained that we stomp and bang around in the early morning. The quiet hours for the community are from 11-7, we are asleep during that time! We went down to try and talk to her politely and even offered to give her our cell phone number to call if there is a problem. She was rude, said it must be our dog (which it can't be) and admitted she doesn't know what time the banging is occuring since she sleeps until nine and doesn't bother to look at the clock. I think she is hearing us get ready, after seven, and it annoys me because I don't feel we have any recourse to prove we are not making noise. How to we defend ourselves? If she complains enough, we could get evicted!How to deal with a false reports from an apartment neighbor?
Write a formal response including the details of what she said. Keep a copy of her complaint and if it continues, file a harassment charge with the police. I'm sure she will stop once the police come knocking on her door.