You are basically dealing with rough line art, could actually look fine on paper or a bmp but just does not translate well to CNC etching. You cannot get the fine details, depth or color/shades that are required to make something like an animals face look like it does in a picture. For that, you would need to do a lithograph where it would come out exactly like the picture right down to the whiskers, but you need aspire or photo vcarve for that.
I have only seen 1 guy 1 time in the past 7 years produce a decent plexi etch of a person [animals are even tougher IMO], maybe someone could post a link to that old thread if it rings a bell. Not that that would help here, but an interesting read an offers inspiration for those interested in doing this.