Perhaps think about using a pressure sensitive graphics tablet and stylus, such as a Wacom. You could use it in Illustrator to ink over the top of a scanned sketch.
That's certainly one way to achieve that slightly wonky hand drawn look, and I suspect that is how she may have made some of these, although many also look like normal vector work easily achievable with a mouse.
Another possible option is to ink your sketch with black pen on paper, and erase any pencil lines. Scan it, then auto trace the bitmap image in Illustrator.
Also there's nothing to stop you from using actual scanned hand-drawn work on the web or in print either. You could scan it at 300dpi (or higher), and clean it up a bit using raster image editing software such as Photoshop/GIMP etc.