It's been a month and he still can't quite believe it. It doesn't fit with his view of the universe that this smart, beautiful, wonderful woman should be showing any interest in him. It's just not supposed to happen, and yet here they are. She's sitting on his couch flipping through a book, waiting patiently for him to make himself presentable after a long day (and night and day) hunched over his dusty books. She's been working too, but she remembers things like sleeping and changing clothes, so she looks perfect.
He doesn't understand what she sees in him. He's never been particularly shy, but neither has he ever been good with women, not when it comes to dating. It's only by her actions that they're together, and he can't imagine why she cares enough to bother (one thing he is good at is self-deprecation), but he's not about to ask and risk her realizing that she's made a mistake. Maybe the universe has changed its mind and decided that it's okay for Daniel Jackson to be happy for a little while, but (even overlooking the fact that he doesn't actually believe in fate) he hardly dares to hope that that's the case.
And yet, for whatever reason, he really is happy right now. He loves his work and knows that he's making progress, seeing connections no one else has. There are people around him who he genuinely likes and respects, and they seem to have a similar opinion of him. And then there's Sarah in his living room waiting to go out to dinner for their one-month anniversary (The linguist in him notes that "anniversary" is by definition a yearly thing, so it really makes no sense to talk about a one-month anniversary, but he doesn't say anything because, contrary to popular belief, he doesn't say every single thing that pops into his head). And he hopes against pessimism and past experience that just maybe this happiness will last.