The answer to your question can be found in chapter seventeen, when Jen and Luke are talking in the aftermath of Luke being unable to contact her the previous day, which concerns him greatly.

When Luke asks her where she had been, she explained casually that her mother had made her go shopping. Given that both Jen and Luke's existence is illegal and must be hidden at all cost, Luke is astounded that she was able to go out. However, Jen's family is rich and influential, and this opens doors.

I would argue that Jen has two things that made this possible. The first is a forged shopping pass that her mom had gotten for her sometime earlier. According to the pass, she is her mother's niece. While this document is good enough to fool store clerks and allow Jen's mother to take her dress shopping, she also tells Luke that if the Population Police ever had to take a look at it, she'd be dead.

The second thing that Jen and her family have acquired is a vehicle modified to hide somebody. She explains that she got to the mall by hiding in the hollowed-out backseat of her family's car. Finding out that Jen has been out immediately gets Luke wondering if he could do the same thing by hiding "under burlap bags in the pickup truck bed."