In the same universe as 'AU'. Still interested? I'm wondering if I should make it its own story.
Disclaimer: If I was Mr. Moffat, I'd be a better writer.
"So, where would you like to go?" the Doctor asks, standing by the console. She looks tense, nervous, and she sounds like she's reading from a mental script. "This machine isn't just an instant airplane, you know; there's many different worlds out there."
"You mean... there are other aliens?" Rose asks. "Not just your people?"
"Well, yes," the Doctor says, laughing, "though they like to pretend otherwise."
"Take me somewhere... spectacular," Rose says wildly, laughing too. "Take me to the ends of the Earth."
"Your wish is my command," she says, and she's off, spinning things and pressing them, moving with a very precise grace. The column goes up and down, and there's a bit of creaking, but other than that Rose couldn't tell they were moving at all. She looks around at the interior of the TARDIS. "Bit gothic, isn't it? Kind of gloomy."
"It is, isn't it?" said the Doctor, frowning at the nearest column. "I don't know why I haven't changed it yet. Sentimental, probably. Well, some wallpaper should fix that! We can do it when we get back!" She's so chirpy, Rose thinks, at least when she's not all tight and nervous. And she's waaay shorter than me.
The column's stopped moving. "Where are we?"
The Doctor smiles and gestures. "See for yourself."
Rose walks out into a brown-paneled room. "Oh," she says, trying not to sound disappointed.
The Doctor laughs at her, and flashes her sonic screwdriver at a panel. Suddenly, part of the wall rises, and she's left staring at the Earth. The Earth as seen from space. It's... glittering, and huge, and beautiful. But.. it's also wrong. Something's different. After a moment she realizes that what's different is the sun. It's huge, and red, and malevolent. As she watches it flashes orange and expands.
"The end of the earth, as commanded," the Doctor told her. "Five billion years in your future."