All animators are doodlers. Typically they start at school and draw pictures in their notebooks when they should be listening to their teachers. People bored at meetings doodle, and graffiti is a form of doodling. It is one of our natural instincts that has never really been utilised for education.
There is a clear cut distinction between doodling and drawing, with doodling it is organic; a shape grows without real purpose. Quite often it is a letter or shape that exists, and it vaguely reminds you of something so you add a bit here and there, and then it takes on a form of its own.
I once wrote a book called 'How Do You Doodle' based on using letters, numbers, and simple shapes as starting points for children to create pictures. The numbers 0 - 9 can all be easily used as noses (www.makemovies.co.uk) As writing developed from pictures, it does not take much imagination to reverse the trend.
An interesting site is at http://www.zefrank.com/gallery/dtoy_gal/index.html which has some animated shapes you can doodle with. Although these are limited, they make a good introduction to animation for children.
Another fun site is at http://www.morphases.com/editor/ This doesn't require any drawing skill, but allows you to change the facial features around in many ways.
Although it calls itself Morphases, it isn't actually morphing in the way animation changes a picture from one shape to another. An introduction to the principles of animation can be found on http://cartoonster.com/ It is one of many sites that show basic techniques.
There are very many 'Morphing' programs used for Special Effects (SFX), but the idea was first popularised in Felix the Cat going back to the earliest days of animation. And of course the Aardman Animation creation 'Morph', the little clayman who could change himself into anything, and initiated the highly successful 'Creature Comforts' and all that followed.
Other Doodling sites: Doodle