Appartment or little house in Central Copenhagen

Hello, we just got amazing jobs in Copenhagen City Centre, and now me and my partner (German-Swedish) would love to find a new home for us and our lovely indoor cat on a permanent base as soon as possible. It would be great if there would be two bedrooms so we can also have guests. A little balcony or garden would be nice, too. We don't have any children but we would love to be able to listen to music without disturbing the neighbours. We are willing to pay up to approx. a 1000 Euro including all facilities per month, and we are also very tidy, clean and reliable in general. We are looking forward to hear from our new landlord soon. (-: