The narrator's daughter is more important in the text for what she represents than for who she is. We never really get to know her at all—she's too young when she's abducted to speak in the narrative, or to even be named. Only a few details stand out, like her light-blond hair and the way she smelled at bath time... but they're enough to totally break our hearts.
When the family tried to cross the border, the little girl had her "two best dolls, her stuffed rabbit, mangy with age and love" (14.38). But while the narrator says, "I know all the details" (14.38), she shares few of them with us.
Sometimes the narrator refers to her daughter as simultaneously dead and alive. "The little girl who is now dead sits in the back seat [...]" (14.38). For the first portion of her narrative, the narrator clings to these memories of her daughter and hopes that she is alive and healthy, wishing she is "a girl [...] who still does exist, I hope, though not for me. Do I exist for her? Am I a picture somewhere, in the dark at the back of her mind?" (12.13).
It's impossible for the narrator to separate her desire for her daughter's well-being from the question of whether her daughter remembers her. Even though she can't have her daughter, it might be almost enough to know she exists and remembers her mother—just as the narrator preserves the memory of her own mother.
But if the machine of Gilead has worked so well on brainwashing adults, eradicating so much of their own memories, imagine how powerfully it could work on a little girl. The last time the narrator sees her daughter—in a photograph—the girl is identified by what's missing, the knowledge of her mother:
I have been obliterated for her. I am only a shadow now, far back behind the glib shiny surface of this photograph. A shadow of a shadow, as dead mothers become. You can see it in her eyes: I am not there. (35.35)
This is worse for the narrator in a way than if her daughter had died. Although it's only been a few years since they were separated, they aren't going to be reunited. It's as if the narrator has died; she is a "dead mother." The picture, more than anything else, seems to finalize the loss of the life the narrator led before.