You can read a good discussion of the trace function here. And in addition there are modifier keys (option or control, can’t remember which) that you can hold down while clicking the mouse, to change the contrast and get more of the interior area. Also, I’ve noticed that auto trace can be a problem if the picture/object you are tracing is glossy.
In this particular case, here is what I would do:
Click once outside the figure to get the outside cutline and interior engrave area. Don’t worry if the engrave has a hole it it.
When you get to the working screen, you will have two operations—a cut outline and an engrave operation.
Click on the Engrave operation and change it to Ignore.
Click on the Cut operation and change it to Engrave.
Place your design on the material where you want it to engrave.
Run the Engrave. When it is done, without moving the material (very important!), go back into the interface and change the Engrave operation back into a Cut operation, and run it. The laser will cut the outline.