Superwho and Impardis too

The quake

Sam and Dean were at the store when it happened. It was different than all the other earthquakes. Sam put $100 on the counter for the estimated cost of their things. They were running out, dodging anything that fell. As soon as they got outside, the earthquake stopped.

The two hunters walked slowly around the parking lot, gazing at the dented cars, looking for where the impala-Baby- was. Dean started to freak out as they neared where they parked.
When they got to the spot where the impala was, it wasn't there. All that was there was a woman sitting cross legged in the middle of the space.

When they got closer the girls eyes got wide with excitement and Deans eyes got wide with anger.

Dean opened his mouth to yell at the woman, but she spoke first 
"Heyya, Dean!" She said in a southern Kansas accent.

"Uh, hey." Dean said. "Do I know you?" He inquired wondering if they had slept together at some point.

"Did the uh," she went down to a whisper. "Angels wipe your memory again?"

"What?! No. We were just bringing Cas and Gabe some food, wait. You're not one of our crazy fans? Are you?" Dean questioned. He almost felt safe with this strange woman.

"Oh, no. Those a books are interesting, but not as cool as actually going on all the adventures with you."

Now the Winchester brothers were confused. Sam called Bobby to pick them up.

"What'd you idjits to to that car this time?" Bobby asked.

"We uh, it's kinda funny actually. We didn't do anything. Just come pick us up and we'll explain later." Sam said holding back a laugh as Dean made multiple moves on the girl and she turned him down with disgust.

At Bobby's
As Bobby hung up the phone he called to the two angels residing in his home.

"THOSE TWO IDJITS CRASHED DEANS CAR, ILL BE RIGHT BACK!" He yelled and walked out.

A little while later there was a knock at the door. Cas cautiously answered.
"Hello," said a strange man with a British accent and a bow tie as he barged in the door followed by a woman in a poofy blue dress. "I'm the Doctor, and this is Tardis." He gestured to the woman. "Judging by the house I'd say we're in the Singer household in 2010." He stated.

"What kind of doctor are you?" Cas asked.

"A good one." He replied holding up his psychic paper to Cas.

"Why are you showing me a blank piece of paper?"

The Doctor drew the thing back and looked at it, then Cas, then it again very confused. "Who are you? What are you?"

"I could ask you the same thing." Said a new voice belonging to the archangel trickster, Gabriel. Cas just stared at this interesting bow-tied british man.
"We crashed and landed here and now the Tardis is human, again, and we are here. I'm a Time Lord and I travel through space and time in my big blue box called the Tardis, but now she's human." The Doctor explained. "And I don't know how it happened. "

In the parking lot

Bobby pulled up to the store where he saw Dean, Sam, and a woman.
"And who might you be?" He asked her.
"Hi Bobby, I'm Baby." She answered.

"Baby? That's an interesting name." Sam wondered out loud.

"Well get in, we'll get you to my house and get you cleaned up, you look like you could use a wash." Bobby told Baby.

As they drove, Baby kept talking about hunts that Sam and Dean have done like she was right there, watching. This made them very confused.

Dean whispered to Sam,
"Another profit?"
"Possibly, but I have this feeling that we know each other, like really well" Sam replied.
"Yea, me too."

They arrived at the Singer home to hear a British voice laughing along with Gabriel and Castiel's.

"Cas?" Dean asked
"What Dean?"
"Who the hell are they? And why are they here?"
"These are the Doctor, and Sexy." Gabe says, gesturing toward each individual as he states their names. "And they are time travelers," Gabe continued. "And who's she?" He points the Baby who's inspecting every inch of the entry way.

"This is, uh, Baby" Dean said rubbing the back of his neck. "She was where our car was. "
There were confused looks from everyone except the Doctor, who look surprised and relived.

"Baby, come over here for a moment. "  the Doctor called.
Baby strutted over and the Doctor put her next to the Tardis. Then he pulled out this stick thing with a green end. The end glowed as he moved it through the space around the girls.

"Ah hah!" The Doctor said. "I think I know what it is!"

"What is it?" Cas asked the obvious question.

"What time did you find her?"

"Uhh, oneish. Why?" Dean replied.

The Doctor mumbled counting on his fingers, deep in thought. Then his eyebrows raised in realization. "Where was she?" He asked Dean.

"Uhh, sitting in the parking lot. " he said clearly confused.

"I KNEW IT!" The Doctor yelled. At that, Baby jumped.

"Baby, do you know how you got to the parking lot?" The Doctor asked.

Before she could answer Sam interrupted. "You know what?"

Baby shot him a glare. "Dean brought me. I've been trying to say that. " she said.

"I am correct. At the time Tardis turned human -again- Baby -your car- became human too. " The Doctor simply replied.