I absolutely love this. You can feel the awkwardness of the moment. It must be so hard for the Doctor because he's looking at River just after having watched her die and he can't tell her about anything. River is, of course, as wonderful as ever. You write her perfectly.
I like this on Teaspoon too :D they are magnificently awkward! I really like how you capture how the Doctor is still getting used to things like comparing diaries that are old hat for River :(