Chris, my DD 25 mos. is like yours.. big circles mean anything worth drawing.
Part of my DD's problem is me - I have refused to let her have crayons. She eats them. But we just started finger painting last week and also started using crayons for the bathtub.
Tonight she was doodling in the bathtub. "I'll draw you, Mama," she said and she passionately put down wild scribbles. Then she drew another one that was distinctly a round head and my long hair and two eyes. I was SHOCKED. I said, "Wow! Can you draw my smile?" but instead of a mouth she drew a tight little squiggle over my forehead and then said, "There is your smile and here are your wings" and drew two wings behind me. "You're an angel," she said. Hmmmm. Last time I checked I wasn't dead. (What she lacks in hand skills she more than makes up for in imagination.)
DH and I are both artistic and I have every art supply you can think of. I'm just waiting for DD to stop eating things so we can do art together all day long!
My MIL 82 has a notebook her father made of her early drawings. They are titled and dated and show when she could draw a head, body, eyes, etc. It is an amazing addition to her baby book!