It is more of a wry, fatalistic, and sad smile, as when she sees young Cole at the Airport, she finally puts all the pieces together from what Cole had told her.
In the theater, Cole falls asleep and remembers/dreams seeing her running in the Airport. He wakes panicked, to find her gone. He runs into the lobby to see her as a blonde, just as she was in his memory/dream.
He says "It was always you. In my dream, it was always you."
In a sympathetic response, she replies with "I remember you like this."
Cole becomes confused. "You do?" he asks.
She says "I felt I've known you before. I feel I've always known you."
Cole's confusion deepens, and he replies "I'm so scared."
That scene is important, because it shows how she has really turned that corner, in believing and wanting to believe what Cole tells her. She feels it is more important for him to understand that she is with him. More importantly, she wants to believe him, to the point of making herself think she has indeed seen him in the past and her dreams.
For Cole, he knows to some degree that his dream is founded in a memory, and he knows he has traveled through time. So for him, dreaming and remembering her at the airport when he was a kid is more of a revelation when he sees her as a blonde. What confuses him so, and begins to scare him, is when she not only agrees with him, but tells him that she has always known him as well. Cole knows she hasn't traveled through time. Cole knows she couldn't have seen him in her past. He may even begin to doubt his sanity, and his dreams/memories at this point... for he had previously believed that it was a memory. However, if what she was saying was true, that she really felt like she had always known him as well, then he might not be remembering things.
So, later, at the airport, when she sees him as a child, the last pieces of the puzzle fall into place for her. She knows that she is doomed (along with most everyone else) because he was telling the truth all along. Any lingering doubt she had at that point has washed away. She knows he was telling the truth in the theater when he said she was in his dream. She knows that she scared and confused him by telling him she had always known him. It's an OMG moment for her. She knows that he survives the coming wave of death, only to be sent back to die before it happens. The futility of everything they have done settles on her, and it all comes out in that smile.
So, I wouldn't say that the smile is honestly a happy one, except in that she was relieved to know the man she fell in love with wasn't crazy after all.