I don't want my girlfriend to housesit
Is she untrustworthy? Why don't you want her to housesit?
I want to be with her every moment. I'm afraid she might get raped by neighbours
I know you love your girlfriend and it's good you're concerned about her safety, but you don't want to smother her. You should strive to be less dependent on her and develop other interests and friendships.
I think she would be insulted if I don't want her to housesit.
Then wouldn't it be best to let her housesit and not baby her around? Having privacy and time off from each other can create an even healthier relationship. It's great that you are worried, but you can just warn her and look out instead of clinging to her.