I'm going product of Amy and the TARDIS.The little girl, well the ending, has Moffatt made it his goal to destory Galifery Base, and Who fandom generally? that is amazing, suggests the girl is the product of Amy & the Doctor.
I'm thinking it'll be something else - like she somehow stole the aborted regeneration from when she shot the Doctor. Seeing as she says exactly the same line that he said to her last week. (and, yes, I know that was in 2011, not 1969, but how did she get to NYC on her on anyway? I think we're going to see her again and she'll get some time travelling)
Oh, and as for the Doctor's invitation - you'd think he'd recognise his own bloody handwriting!