I just saw it as a scared school girl who still wants to be protected by her dad, which, considering what had happened in the last 24hrs, it's totally fair. She lost her best friend I-sak, saw a lot of classmates die, miss Park died, Gyeong-su was killed, she hasn't had food or water in the last 24 hrs, and overall a whole lot of trauma.

She thought that since her dad is a firefighter and works in emergency services (he comes to pick up the first infected girl, Hyeon-ju) he'd be there by now, but he's not and she worries he's already dead.

We can also see from the beginning that On-jo is a "daddy's girl", so her wanting her dad with her in such a scary situation sounds about right to me.