RigasThat's pretty much my theory so far also, and the whole River being married to the Doctor time span. I think that the child will eventually regenerate into a young river and the Doctor will know all about her at this point and drop out of the sky to take her away and teach her about what she is. This will probably take many years which is what has been the "marriage" between the two. (note haven't seen ep 4 yet)
As to how Amy's child gets those abilities ( time head ) I still haven't got a satisfactory theory yet.