As you look in more detail at its meaning you get, to 'scrawl aimlessly,' back in 1935 this use it was suggested was perhaps coming from dialect, the terms doodle and dudle were used to express an idea of 'frittering away time or a trifle.' It was also associated with the word dawdle (which might be the source of the dialect word). But it is interesting that its history is one also associated with cutting or slashing. To doodle is also a verb, a doing word. The noun, 'scribble' as in 'hurried or careless writing,' is from the 1570s, and was derived from the verb to scribble, gradually this came to represent careless or overly fast drawing as well as writing. To scribble is a word that comes to us from the mid15th century and it derives from Medieval Latin, scribillare, a diminutive of Latin scribere 'to write' (from Proto-Indo-European *skribh- 'to cut'). There is an interesting difference between the activity of 'scribbling' which is defined as to draw carelessly or hurriedly and doodling, the making of drawings while a person's attention is otherwise occupied.

Doodle art means