Damon had been expecting this request, and was actually surprised it hadn't come up already.
"When you've learned a little more of what you're doing, then yes," he replied. He knew that he couldn't keep her holed up in her room forever, and even if he tried, Stefan would crack and let her out sooner.
"You need to know enough to stay out of other people's way, and where you can and can't go. Did Stefan give you a tour?"