The Doctor and Rose find a baby outside the TARDIS. What happens next?

The TARDIS landed in Cardiff just below the big sign, near the rift, as always. However, they found something unusual that would change everything.

Just as they stepped out, a baby's cries caused Rose's head to turn to the right. There stood a stroller with a bundle in a blue blanket. The duo walked forward, and upon further inspection, discovered a newborn (less than a month old) baby boy. A small diaper bag hung from the back of the stroller, and pinned to it was a note that read Please take care of him. Heaven knows I can't.

Rose and the Doctor shared a look, and knew they had to care for him. They brought him inside, and the Doctor began to examine him while Rose took stock of the diaper bag.

"A boy, less than ten days old-"

"How do you know?" Rose asked while she rifled through the bag.

"Regardless of species, genitalia tend to stay the same between humans and Time Lords," the Doctor deadpanned as he put the diaper back on.

Rose rolled her eyes at his remark. "I mean, how old he is? How did you know?"

"His umbilical cord is still attached. It tends to fall off between 10 and 21 days. "

Rose nodded at this. The Doctor then proceeded to weigh and take the baby's length, and document this as well. He examined the baby's eyes and ears, and then decided to listen to the baby's heart and lungs. When he listened to the boy's heart, a furrow in his brow caused Rose concern.

"What's wrong?" Rose asked.

"This baby is half Time Lord. Listen." He motioned her to come over and listen to the baby's heartbeat. Rose set the bag aside and listened. It had two heartbeats. She turned to him with a shocked look.

"I thought you were the last surviving Time Lord," Rose said.

"I did, too. I ran his DNA, and I'm not his biological father. This just gets even more and more bizarre," the Doctor mused. "Not that you're bizarre, of course not. You're just too cute for words," he then said to his son before turning to Rose.

"What do you want to name him?"

"Well, it would be nice if you told me your real name so I could name him after you," she suggested.

"Not happening. He will be scarred for life if you did. He gets a human name, Time Lord or not."

She thought for a moment. "How about David? David Tyler Smith?"

"Sounds fine to me," he said as he handed the baby off to Rose so he could input the information into the "chart" he started for the child. "So where do we stand on supplies?"

"We have four diapers, two bottles of formula, one pacifier, and an onesie, a rag that can be used for burping, a blanket, and a note that said that he was fed at 13:15 today. We should probably get to a shop."

"That might be a good idea. We can also check the wardrobe for clothes," the Doctor said as he stood up. He studied his son's red hair. "How come you get to be ginger and I don't? Oh well, it might be short-lived."

"What do you mean?" Rose asked.

"Babies are sometimes born with red hair, and then their color changes as they get older. We'll see, though. Shall we go?" the Doctor asked, getting up from the captain's seat.

"Sure, let me get the stroller," she told him as she went into the closet in their room.

They went to a nearby shop and bought enough baby essentials to last a couple of weeks; diapers, a couple of outfits, formula, bottles, pacifiers, onesies, and wipes. The Doctor told Rose he still had his old cradle, so they could use it for now; they would buy a proper crib later.

"The clothes look a bit big," Rose commented as they left the store. She sat down on a nearby bench to give David his bottle.

"Children grow like weeds. These will last a while longer. Anyway, we should check the wardrobe to see if we have anything in the way of baby clothes. "

"I think we should talk about who should be David's godparents. I'd like Jack to be his godfather."

"Jack? As in Captain Jack Harkness? Are you mad?"

"What? He's a good man. I think he'd be great with the baby. Let's ask him and see what he thinks," Rose said.

"All right. What about his godmother?" the Doctor asked.

"What do you think about Donna? Do you think she would make a good godmother?" Rose asked as she was about to burp her son. The Doctor offered to take him and put him over his shoulder.

"Sure, she sounds like a good choice. Don't get me wrong, I love Jack like a brother, but him as a godfather?" HHe asked with a shake of the head as he coaxed David to burp. Once this was accomplished, he placed him back in the stroller and wrapped the blanket around him tightly to keep him warm. With that, they were off to Torchwood to pay a visit to their friend.

Author's Note: I picked the name David for the baby partially for obvious reasons, but also because a) I like the name, and b) after my godfather. It's also kind of sentimental when you think about it (it means "Beloved" in Hebrew). I was born with red hair, and then it turned dark brown. About the cradle, if you've seen "A Good Man Goes to War", you'll see that the Doctor brings out his old cradle when he insists that baby Melody is crying because she's tired.