9 days stay in Copenhagen, look for short term rent

Hi 

I'm a PhD student from London, I'm going to Copenhagen for conference in the summer. I realized the money I spend in a shared room in hostel is even enough to rent a room for one month, so I decided to look here. 

I want a private room with ready to use facilities, 9 days are a long trip so I want to feel at home. Preferably with a desk and within 30 minutes walking to the city center.

Cheers

Yan