We don't set time limits (but we do have to share, so there are some associated limits). When DD was a baby, we let her play with the computer perhaps once a week for five minutes or so. I would _never_ have left her alone with the computer at that time, and she is still not entirely trustworthy. By now, my computer is taped together and missing several keys. She learned to use a mouse at the same time she learned to use a touchpad. I think she was 2, perhaps 2 1/2. By the time she was 3 she was truly independent on the computer.
I would discourage thinking of a computer as a babysitter. It is very important for preschoolers to learn to play by themselves, but it's totally normal and appropriate for babies and toddlers to want to interact with others all of the time. If you are tired of reading, by all means, do something else. But a computer isn't going to do more for a baby than a TV would, IMO. FWIW, DD began wanting to play by herself in her room for about ten or fifteen minutes at a time when she was about 18 months old.
