Doodly means having a doodle-like style — simple, casual drawings that look like they were quickly sketched by hand.
In:
All wrapped up in a doodly art style
it means:
Everything is presented in a cute, hand-drawn, sketchy art style.
noun verb
doodle
to draw lines, shapes, etc., especially when you are bored or thinking about sth else （尤指厌烦或心不在焉时）乱涂，胡写乱画
I often doodle when I’m on the phone.
我打电话时常常信手乱画。