The program's PaintTool SAI. It's easier to use than most softwares. The trial is free, if you search for PaintTool SAI in Google, the official site should come up and you can download the trial from there.
Wow, if this is called doodling then I'd be even glad to call mine chicken pen scratches. The eyes are really lovely. For me, eyes (along with hands) are always the trickiest things to draw. One little stroke changes everything. Awesome work