I just bought a 7" Android tablet for my three year old son. I thought a small tablet would be easy for him to use, but there were some surprises when I observed him.
The battery in a 7" tablet is still too heavy, so he just sits with it on the floor like he's reading a big picture book. The 10" size is probably better--especially if the touch targets are larger and less scrolling is needed.
The touch UI generally works very well, but multi-touch has caused a lot of frustration. The sexy flush screens that are popular now hurt usability because there's no tactile feedback that his fingers have creeped onto the touch surface. Many times he was frustrated because a touch wasn't detected (or was treated as a multi-touch) due to an errant thumb sneaking onto the edge of the display. A physical ridge or lip around the screen would really help even if it would be a bit ugly. Disregarding that hardware issue, there are still a few problems.
A small child's body has different proportions for arm, hand and fingers. My son found it easier to use his thumb to tap because he could see touch targets better. He also experienced lots of false multi-touches with his index finger because the fingers curled up under his hand would brush the screen. His arms were much closer to parallel to the display than mine were, so he compensated by using a thumb (and keeping his fingers out flat) or by using his index finger at steep angle.
Only a few gestures were intuitive: tap an object, drag an object and drag the background. The background drag had a funny side-effect of wanting him to hold his other hand flat on the screen to "stabilize" the background when dragging an object. Obviously that didn't work and frequently confused him with a multi-touch activation. In the real world, holding your hand on paper will keep it still, but in the computer world it causes random magic. Tap worked well, except when it wasn't obvious what should be touched. My son usually tried to touch where he expected something to happen, then touch harder (and harder and harder!) before giving up to try something else. It's too bad the touch screens don't recognize position and force.
Lastly, the Samsung Tab he uses has poor physical button layout for a child. The power and volume buttons are on the side of the tablet, and four flat touch areas are on the bottom (or side) of the screen in the bezel. He occasionally hit one of these without realizing it and was confused by what happened. I don't think the design is particularly bad just for children--it seems pretty bad for everyone.
I'm really pleased at how well he's been able to use the tablet and I definitely recommend parents to try a tablet with any child able to use a picture book.