Frederik was quick to respond and was very accommodating (e.g., with flexible check-in times). His apartment was quiet (great for sleeping), clean, nicely decorated, and filled with the amenities listed. While the apartment is on the smaller size and in the suburbs (as listed), it is a fine size for 2 people and is an easy walk to two Metro stations (though the cobblestone sidewalks are a little tricky to navigate with a suitcase). From the Metro stations, you can easily get anywhere both in and outside of the city.
We had a great time in Copenhagen and would fully recommend Frederik's place.
One note if you plan to do laundry though: leave yourself some time. The washer is finicky: it takes a while to wash and sometimes, you need to re-start it (so you need to be present when running it). Also, there is no dryer, so you will need to hang up your clothes on the provided rack (so leave adequate drying time).