Disclaimer: If I owned Doctor Who, this would actually happen :)
The lullabye the Doctor sings is from the movie Move Over Darling with Doris Day and James Garner. Great film!
The Doctor leant over the cot of the cooing child, a tired worn out expression on his face.
"Come on now little one," he said, punctuated with a yawn, "me and mummy need our sleep, as do you"
He bent down and picked up the baby, cradling it in his arms, holding him close to his warm chest.
"shh shh shh" he whispered looking down at the small child who was looking back at him with large blue eyes and a huge, toothless grin. He felt his hearts melt.
"I'm gonna have to sing you a lullabye aren't I little one?"
The Doctor smiled at the gurgling child in his arms. He began to sing, slowly, gently.
Stars up in the sky
Time to sing a lullabye.
Sing you a song,
Of a toy balloon,
Sailing far across the moon.
Go to sleep,
And very soon,
You'll be like that toy balloon.
Deeps in dream land,
Far beyond the sky,
Twinkle, twinkle, twinkle hushabye"
He smiled. In those few minutes of gentle singing he'd managed to get his and Rose's child to sleep, a feat he was extremely happy and proud about. He was getting used to the whole father and domestic scene now, although he really didn't want Rose to know. He liked to protest against domesticity, yet here he was, child in his arms once more, with a woman he loved with both his hearts in the next room. If he was truly honest with himself, he couldn't want more.
He leant over the edge of the cot and laid his baby son in the cot, and stopped to pause and look at the sleeping infant.
"You're gorgeous little one, just like your mother"
"And he's cute as well as handsome, just like his father." Rose was standing in the doorway. She'd woken up and found he wasn't with her, and she knew the only place he could be was in the nursery.
"How long have you been standing there?"
"Long enough," Rose said with a smile.
Smiling, he held out his arms for Rose. She walked over and snuggled into the Doctor's chest, arms around his waist, his arm around her shoulders.
"I love you, you know that right?" the Doctor whispered so not to wake their sleeping child. He felt her smile into his chest.
"Mhm, and you know I love you too, yeah?" she whispered drowsily.
In reply, the Doctor kissed her head and mumbled into her hair, and ran his hands through it.
"Let's go back to bed," he gestured, "Junior's asleep now."
Rose smiled, "Yes, lets."
And still snuggled together, they walked out of the room, but not before pausing at the door.
"You know Rose, we really should name him. We can't call him junior forever."
"I told you, I want you to name him. He's half Time Lord after all, and a human name just wouldn't do complete justice to who he is."
"I know, but you didn't like what I suggested before."
"And quite right too. I'm not calling my son Alonzo, just so you can say 'Allons-y Alonzo' everyday." Rose's voice had raised itself slightly, and the baby stirred.
"Let's talk about this later. Maybe the TARDIS can help decide." The Doctor said, possibly slightly heavy hearted.
And they shuffled out, into the corridor and to their room next door.
The TARDIS hummed gently. She produced a small name plaque on the nursery door. In Gallifreyan and English was the name 'Aaron Sigma Tyler' the perfect name, for the perfect child.