There are many challenges and opportunities in shooting little ones.  When they learn to walk and ask for things, the game changes.  That being said, they now are more responsive and expressive to your gesturers and attempts to make them smile.  While none of this is a substitute to a professional photographer, these tricks will help you take better shots of those little friends in our lives. 

Get on their level.  GO ahead and lay down, squat and play on the floor.  Thy will look directly into your lens and you are more likely to catch the lights in their eyes.  You are also more likely to capture a sense of scale and proportionality.  

Position them on adult furniture or in more mature environments.  When shooting children it is important to see the world as they do, but also to show them as small and vulnerable.  Putting a kid in a kids seat just makes them look proportional to the world that is much to big for them.  If you take that same shot and insert a large ottoman or kitchen, suddenly your child looks small.  The success of these images depends on the relative environment.  

Give them something to hold into, hand them props and accessories.   For boys this can be hats and toys, for girls it is everything from wands and jewelry to a chair to position themselves on and around.  Giving a boy his dads hat can take the pictures from good to great.  The hat will flop around and be to big, but that is just the point.