Is the underscored line natural as it is?

Hi there.

She pulls up outside his house and he gets out of the car. He waves goodbye to her, then turns and heads to the house. She watches him go, missing him more with every step he takes. He gets to the front door, unlocks it, and steps inside.

Is the underscored line natural as it is in the context or would you add "up" after "heads? Or replace "to" with "towards"?