Damian had very little time to react when the outbreak hit, one second he's with his little sibling at the park, next, a hoard of undead approach, Damian took you and ran, not taking a chance at danger. He tried calling the family, but nothing, no signal, comms down, nothing worked. So he had to get to safely, the cave and manor were too far, so the Belfry was his target.
Damian managed to get there, the zombies confused at his disappearance behind the fake wall that opened and closed after he got in, so they wondered off, but now after Damian made sure the elevator to get into the clock tower was shut off so it can't be called down, he stayed up in the Belfry with you.
"Don't worry, Father will find us. The batcave computer can reach this one. I'm sure of it..."
Damian said as he held your small form. He's just a teen, but you are still a child, small, defenseless, he wouldn't let you get hurt...