How can I be supportive to my girlfriend (a rape victim) while still maintaining my independence?

I have been dating a girl for around 3 weeks and we really seem to have a connection. We share a lot of the same interests, both have an easy going personality, and have a lot of physical/sexual chemistry. She seems to be a great girl but is giving signs of being a little bit needy. She wants to hang out with me almost every day which is too much for me. I am a person that values my alone time and independence a great deal. I enjoy spending time with her..just not every day. She revealed to me toward the beginning of our relationship that she was a rape victim and also the victim of a separate incidence of sexual assault. I really feel for her because she is a great girl who has had some very bad luck during her lifetime. Despite all of her hardships she is an optimistic and fun person with a lot of strength. I have the utmost respect and admiration for her. I feel a connection with her. I just fear that her needyness may drive us apart. I know that rape victims often have a hard time being alone so I'm sure this has something to do with the situation. I want to make this relationship work if at all possible. What are some things i can do to be supportive while not being smothered?