My daughter loved "Water, water" by Eloise Greenfield, "Daisy's Favorite Things" by Jane Simmons, and the magazine "Babybug". Another old favorite, which we still read at four years, is called "Rabbit's Bedtime" by Nancy Elizabeth Wallace.
Beyond books, at one my daughter's favorite activities included drumming (she has a small hand drum that she sits on and loves to sing along "boom-boom teck, doom-doom beck"); pouring water using cups and pitchers; painting, playdough, chasing bubbles, knocking down block towers, sweeping, dusting, washing dishes, folding laundry, walking through the wetlands and throwing dandelions into the water, throwing and kicking balls - we also have a huge playground ball that she loved to push around on the grass.
Don't know if any of that will be helpful for gift ideas, but it was sure fun to reminisce. Ask again when she turns 2!