Karen Gillan's cousin, Caitlin Blackwood (not a relation of mine, I should point out), appears as the young Amelia Pond in several 11th doctor episodes beginning with the first: The Eleventh Hour (broadcast in April 2010). She appears again in Let's Kill Hitler (broadcast in August 2011). Her last recognisable appearance was at the end of The Angels Take Manhattan (broadcast in September 2012), although that might be footage from The Eleventh Hour.
The character of the young Amelia appears briefly at the end of The Time of the Doctor (broadcast in December 2013). We see a girl wearing Amelia's clothes from The Eleventh Hour and the Doctor clearly identifies her as Amelia:
DOCTOR: But times change, and so must I.
(The Doctor sees a young Amy Pond run up the stairs, laughing.)
CLARA: Who's Amelia?
DOCTOR: The first face this face saw. We all change, when you think about it. We're all different people all through our lives. And that's okay, that's good, you've got to keep moving, so long as you remember all the people that you used to be. I will not forget one line of this. Not one day. I swear. I will always remember when the Doctor was me.
But we never see her face. The only reason I can think of for that is that it was a different actress. Does anyone know if it was Caitlin or not?
Amelia Pond is not included in the on screen credits (although Amy is). The IMDB cast list lists Amelia Pond as being played by Caitlin Blackwood (uncredited) but gives no authority for the assertion.