Welcome to the forum!
I'm afraid I don't know what an STL importer is. Can you explain?
The best way to learn what you can import is to consult the documentation for your machine and it's software. That should tell you everything you need to know, including which file formats are acceptable.
The image you want to trace is the one you attached? Are you expecting the results of the woodcutting to look like that image? I mean where there are higher and lower places, with a smooth profile? So that it's kind of like a relief map, except instead of the highest place being the highest mountain, the highest place is the dog's nose?
If that's the case, you can't do that with Inkscape.....well, not that I know of. I suppose it's possible that there's some other program which can interpret the result of the trace that you do with Inkscape. But honestly, you'd have to have a super high-end machine to do that kind of cutting. Well, not unless you're already planning to do a lot of hand work also.
Or do you just want the outline to cut out? It's probably better to start with something simple.
You can trace the image using Path menu > Trace Bitmap. From my experience, it takes a lot of trial and error to get a good result. Unfortunately the tiny preview window isn't very helpful. I always have to trace-undo-treak settings-trace-undo, etc.
You definitely will need a larger version of that image. I can promise you that the result of tracing that tiny image will not be acceptable. The bigger the better, and the higher resolution, the better trace result. You'll probably want the drawing to be the same size as you want for the final result. You can scale the trace result before you send to the cutter. But still, the bigger, the better, for tracing.
1 -- File menu > Import
2 -- Path menu > Trace Bitmap
The manual has the best info I've seen about using Trace Bitmap. Plus as I said, it needs a lot of trial and error. I don't think the manual mentions anything about the best options for woodworking, because it was written before these digital and CNC cutters became widely popular and available. Plus, it depends on exactly which kind of cutting you're going to do, which options will be best.
http://tavmjong.free.fr/INKSCAPE/MANUAL/html/Trace.html
