They had to act swiftly, since time was a scarce commodity at that point. The anesthetic wouldn't last forever, and they needed to be well away from the airport before she regained consciousness.
Their destination was a safe house, far from prying eyes and potential interference. Erik knew that once they arrived, Erik would interrogate her.
He hoped that in her groggy state, she might be more susceptible to revealing information about her mother's whereabouts.
As they moved, Erik kept a watchful eye on their surroundings, alert for any signs of pursuit or unexpected complications. The success of their mission hinged on their ability to disappear without a trace, leaving no clues for those who would inevitably come looking for the president's daughter.