A little girl drawing with chalk, on a chalkboard.
A young girl is drawing on a chalkboard.
One has to use a chalk to draw on a chalkboard and little also means young.
A little girl implies a young girl, the girl drawing with a chalk means the girl is drawing on a chalkboard. Usually we write with a chalk only on the chalkboard.
"A young girl is drawing on a chalkboard" is a restatement of a "girl drawing with chalk, on a chalkboard"