As it happens, the introduction of Amelia Pond was not contingent on the arrival of the Eleventh Doctor. Speaking to Doctor Who Magazine, Steven Moffat has explained what his basic story arc for series five would have been if David Tennant stayed on and Matt Smith not been recruited.
Here's his explanation:
I only had the roughest idea. Had David stayed for one final year, it would certainly have been his last, so my pitch was that it would start with the Tardis crashing in Amelia's back garden – as now – and a terribly battered and bruised Tenth Doctor staggering out.
Amelia finds him, feeds him fish custard (no that was for Matt, it would have been something more Davidy) and generally helps him. But we, the audience, can see he's in a truly bad way. Dying maybe. Eventually he heads back to his TARDIS, and flies off.
But when he returns – many years later for Amy – he seems perfectly fine, and indeed doesn't remember any of those events…And of course over time, we realise what we saw was the Tenth Doctor at the end of his life, about to regenerate. Events that we return to in Episode 13…
One of the most interesting things about this are the implications for the relationship between Eleven and Amy, even Rory and River.
Either Eleven would never get to meet Amy and Rory, which would most likely have changed the River Song storyline profoundly, or he'd meet them after they already knew Ten.
Anyway, that didn't happen, and Tennant moved on, leaving us all to wonder what he'd have liked to eat instead of Fish Fingers and Custard.
UPDATE: Thanks to Little Bleeder Ian who sent through the first Amy and Ten photoshop image. That's it at the head of the post. Good work, sir.