Life:
The answer to your question depends rather greatly on the version of Illustrator you are using.
A crude method (as long as all your pencil paths together fully enclose the dog) is to fill the square with a desired color, remove stroke and fill from the dog, select everything and go to the Pathfinder palette (Shitf-Ctrl-F9), click the button that hints "Divide" (Second row, left button in CS/CS2, don't remember where in 10).
Leave everything selected. Object>Ungroup.
Then with the group select tool (white arrow with +), click on the inside portion of the dog and delete. Now, you should have a knockout of a dog in the square.
This method will yield satisfactory results in every version back to v8.
For CS2, use the Live Paint tool combined with Pathfinder tools, Object>Live Paint, explore the options from there.
The terminology for what you are trying to do is "Compound Shapes", in case you want to look it up (Help>Illustrator Help). The Help Files are a mediocre but often helpful resource.
HTH
Bert
