Like children, the Cheshire Cat Book Store is maturing day by day. Even before it opened, its window was hatching butterflies. And by late September it had grown into a charming young thing, a cheerful showroom of books for children and books for parents about children. It has shelves neatly organized with paperbacks and hardbacks, all the Beatrix Potters and Hardy Boys, the Ezra Jack Keats and Carolyn Keene books that no child should miss. It has children's calendars and posters, and stoneware whistles to tuck into gift packages of books. The Cheshire Cat will help you choose books or order books not on the shelves, and prettily wrap them. It is a place for children to browse, or to curl up on a cushion to try a book out. A toddler-size cubby, reached through a keyhole-shaped door, is lined with puppets to while away the time as parents make their decisions. The store encourages not just buying, but also reading, by displaying stories children have written and by planning classes and workshops to make sure those photography and stamp-collecting books are put to good use. A newsletter will review new books. This is meant to be the kind of store where something is always happening - eggs hatching in the spring, new books being discussed, a baby in a stroller contentedly chewing on The Touch Me Book. Cheshire Cat Book Store, 5512 Connecticut Ave. NW. Open Monday through Saturday, 9:30 a.m. to 6 p.m. 224-3956.