That's what I was trying to say earlier with this: "...ink in those lines, then continue to widen and ink in lines." However, besides calligraphy there are techniques where a "line" of varying width is made in a single stroke, such as the Japanese styles using a brush or an expert with an air brush, but I think most illustration is done as you mentioned. (Except not many lines outlines are actually parallel!)
Another thing I'd think about carefully when designing an illustration for carving is how the wider "solid" areas will be carved. For chip carving, for example, lines of varying width are carved as a single V with one sloping cut on each side. Wider or "bumpy" strokes in your example (below) and strokes that meet up with others, such as in the horse mane, at the ears, and the front of the nose might look great on paper but might look sloppy if the intersecting cuts are not planned with carving in mind. Of course, very wide areas can be filled in with textures or something.
What ever you do, I'm sure it will be fun! Get a sketch book and carry it everywhere. Sketch in pencil and ink with a felt-tipped black pen. For inspiration a good place to start might be the cartoons in the newspaper or web or books - look at the lapels on Dagwood's jacket today, the animals in Mutts, the faces and clothes in various comics such as Sally Forth, Zits, political cartoons etc, - some of these artists are experts at suggesting a form with just a few strokes.