Austrian Student needs an apartment for 2 years

Hi.

My name is Valeria D'Amico, I am 24 years old and planning to move to Copenhagen this August (2010) for 2 years as I got accepted at the Faculty of Pharmaceutical Sciences. I am now looking for an apartment because I have a medium-sized dog and I don't want to move into a small room in the university halls with him.

I will drive to Denmark by car and bring my bike so it's not a problem for me not to be in the very city center. In fact I go running every day and would prefer to live in a quiet area near the water or in a very green area of town.
On the other hand, the apartment needs to be furnished because I cannot fit everything into my little car. ;) Internet would be really handy, but other than that, I have no requests.

Please contact me if you can help, in any way!
Thanks for your help in advance!
Valy

P.S. I have heard that many apartments in Denmark still have shared bathrooms - I would prefer to have my own bathroom.