Don't 3 year olds still poop their diapers? I personally would never perform a children's show for younger than 6 years old; 5 is pushing it. Anything younger is simply baby-sitting and a waste of time.
You must engage and hold their attention for 30+ minutes and at the same time, control them throughout the show AND be entertaining.
I strongly suggest you do much more reading and research before you attempt anymore paid gigs with small children; you’re going to give the real workers a bad reputation.
I will definitely agree that performing for children of a young age is more of a challenge than that of their older counterparts; however, it is a worthwhile experience if done right. As you say, it does take more because you do have to understand how to engage them, which requires a whole different skill set than some of our younger members may be accustomed to. I respectfully disagree that it is merely "babysitting".
Children of all ages love and adore magic. When we designed my daughter's magic show it was definitely with family entertainment in mind be it a child's birthday party or a stage show. It is geared towards engaging the whole family from the very young to even the grandparents.
When performing for small children it helps to have experience with working with children to understand their different personalities, which can vary greatly. You also have to design your show with the whole family in mind so that you have something for everyone. As DerZauberer said for the younger ones you must hold their attention for 30+ minutes, control them, and still be entertaining for the group as a whole-- it is not an easy task.
Don't take on a child's show because you feel that will be the easiest--- its not. It takes a lot of hard work, a lot of hours or practicing, in addition knowing how to handle children-- and I'm not talking about how to take care of your little brother or sister.
However, if your show is polished-- and I mean polished-- you will be able to capture a child's attention. Not because you are a magician, but because you are a PERFORMER.