Given the later revelations in the episode A Good Man Goes to War, this moment comes across as almost impossibly heart-breaking. I own nothing.
She's so happy to see him that River can't stop from telling Rory all about her birthday. Ice-skating with the Doctor on the river Thames was just so wonderful and she wants him to know. River's never had much difficulty opening up to Rory and she doesn't at first notice the blank, uncomprehending look in his eye.
"It's my birthday. The Doctor took me ice-skating on the Thames in 1814, the last of the great frost fairs. He got Stevie Wonder to sing for me on the London bridge."
Rory's brows knit together. "Stevie Wonder sang in 1814?"
River nods eagerly, eyes still gleaming bright and open wide. "Yes, he did. But you must never tell him," she adds in a conspiratorial tone, holding a gloved finger close to her lips.
It's not until Rory says he's come from the Doctor too that River recognizes that incredulous gleam in his eyes for what it is, and she knows what he's thinking to himself.
Why is she telling me this?
Immediately, River's demeanor shifts and she's back to mysterious, whimsical and utterly inscrutable. Back to what she knows this particular Rory expects and is used to. The River Song who's not intimidated by something so simple as the Lone Centurion.
Oh, that's right. He doesn't know yet. He doesn't know who I am yet.
After Rory's gone, River pulls the hat from her hair and starts taking the pins out of her hair. She grimaces as the sharp tip of one puts a hole in her finger, but only watches the blood slide down into her palm instead of wiping it away.
She should have known better than for her father to recognize her so early. She just wishes she could have told him a little more about her date.