Definitely. There's a number of blogs dedicated to apps for toddlers. Not sure about a one-year-old, but my two-year-old was finger painting, dragging letters onto words, and rearranging dinosaur parts, and browsing YouTube for videos of trash trucks (he got his older sisters to enter the search terms). My original iPad is basically a dedicated kid computer. The older kids write school papers on it (Pages + keyboard dock), the younger kids play games (educational and otherwise) and sometimes Netflix videos. We do have an XO laptop, and it only gets dug out of the bin when one of the kids is playing "going to work" and needs a faux laptop to lug.
