Symbolism, Imagery, Allegory
Just as Alice escapes down the rabbit hole into another world, David goes into another world by pretending he's Alice.
As a small child, David ties a yellow towel around his head and pretends it's Alice's long blond hair. The consequences for going outside dressed like this are pretty scary—the kids in the park see him hanging from the bars by his knees and chase him away, calling him names like "sissy" and "queer" (1.284). This shows us that not only does David feel different and alone at home, he feels different and alone in the outside world, too. Other kids are no more welcoming or accepting of him than his parents.
The most significant Alice reference in the book, however, is when David imagines his therapist as the White Rabbit. Just as the White Rabbit leads Alice out of the boring human world and into a world of wonder, David's therapist leads David out of the dismal reality in he David finds himself growing up. When we first see the rabbit in Stitches, he's holding his stopwatch, just as he is when Alice meets him. However, this rabbit isn't late for a very important date; he's timing the session, as psychiatrists do.
Note also that when David tells the therapist he's got nothing on his mind, the White Rabbit says, "Nothing? That's curious" (1.27). It's a reference to Alice saying, "Curiouser and curiouser" to describe the world she enters when she goes down the rabbit hole. Luckily for David, like Alice, he eventually finds his way back out.