We found the computer almost a necessity for DD when she was around 18 months because she was a child who didn't nap and was always bringing us books after books to read to her. I didn't like the idea of the television for babysitting and I still question the computer as taking the place too, but desperate times...
She loved the starfall site and we would sit there with her and use that one along with some preschool games, but around 2 (I can't remember if she was 2 or a month short of 2) she took over the controls. She proved to us that she was very independent with the computer and could open up a browser and pull up her bookmarks from the list. Of course the list was long and I was concerned she would get into a site that wasn't meant for her but I also knew that there was no questionable sites in the list. More like boring research about what ever topic I was working on at the moment, but still I kept a close eye on her to make sure she stayed in her bookmarks.
As for time restrictions ... I was concerned about how absorbed she was becoming in the computer and considered a timer for her because it was coming close to an obsession, but she started to bore of it all and started to limit herself. We will go weeks without using the computer and than one day she will decide to get on pbskids.org and spend maybe an hour on the computer and again it will be another week or two before she asks to use it again. I say it really depends on the child. Some will become obsessed with games and computers and will need limits and some will find it useful for a little while and look to do something else. I suspect that if I went out and bought her something new to play on the computer we would find ourselves back into the red zone and see her computer time go up so I might still set a timer for her when and if she does start to obsess over it again.
Suggestion for a mouse: If you are concerned about the mouse being too big for your DD's hand you might want to consider a wireless laptop mouse. They are about half the size, but are fully functional. My DD just used regular size ones and she had no issues.
