First thing to consider is that you will most probably need to have somebody registered as living there permanently.
We manage this my having my address registered at our house outside the city and my husband registered at the city apartment.
The apartment we rent was my husband's bachelor pad before we met. We used to rent it out long to single log term tenants but switched to airbnb for summer 2013 and pretty much trebled our income - but added a lot more hassle.
Your place sounds similar to ours, we only rent it as a whole apartment and in peak season, we make over 2000dkk per night, around 1500dkk over winter. Ours is 110sqm and has two large terraces, one over looking the city and one over looking the lakes. Our minimum stay is 4 nights as minimising hassle factor is key for us. I think the higher price point helps with guest calibre. We mainly attract middle aged and older tourists. We do have free parking available which is also a good USP, but then only about 10% of our guests utilise this. We only have one bedroom and a sofa bed in lounge, if you rent the whole apartment, think about adding a sofa bed so you can up your capacity to 6 people, but think about the additional wear and tear that number of people bring.
I think your price point is realistic, you may need to offer a bargain rate for the first few months to attract bookings and reviews which will boost your search ranking - plus guests like reviews. I think most tourists will search by Indre By and then move out if they can't find anything at their price point. So you will need to highlight your great features, like the water view and terraces but be realistic that you probably won't get the rates central apartments would.
Be aware than when renting by the room you may attract people that are looking to live in Copenhagen and are looking for temporary accomodation while they find a longer term place to stay. There is quite a lot of demand for this.
While living next door will help lower the hassle factor, don't under estimate it. Cleaning an entire apartment is quite time consuming or costly if you get a cleaner. If you're renting by the room, think about the frequency of cleaning of communal areas - especially if you have guests checking in on different days.