I have decided I would like to make the newborn baby a cartoon character in the beginning of my script "It's Not Easy Being Christopher Hungwell" or possibly make the whole screenplay a cartoon. How would I indicate that a character is an animated character or the whole script is animation? Just an idea I came up with.  Marvin.  

You don't.  That's something the director would decide.  You can write in cartoon like actions in order to imply that is what you want.

Like

The baby cries and its eyes bug out until you can clearly see the bulging viens.  

He drops the baby and it bounces off the ground accompanied by a BOING. He catches it on the rebound.

Mcornetto,  thanks for your reply, but what if I wanted the whole thing to be a cartoon? Would I have to make special notations on the script to indicate it was an animation?   Marvin.

Unless it is critical to the story I would not mention it.  It is ultimately the directors decision.  If you were to make it your decision and someone who could make it read it and disagreed then you would lose the sale.  

If, however, you wrote it in a way that forced the reader to come to that conclusion on their own, then you've lost nothing.