CorelDRAW can absolutely do it - but what you’re talking about is not an easy job by a long shot.
I’d start with this video:
Which I got from “the Matrix” which has links to Google spreadsheets with instructions on almost everything for a bunch of different programs.
If that gets you where you need to be - great! We’d love to see what you do.
If not though, there are folks on here who are absolute wizards with vectors, and if you can post a clear, well, and evenly lit photo of the piece one of us can likely return to you a vector drawing with what you need.
There’s also the matter of kerf (which is the width of material that is taken away by the cutting instrument). When doing inlay, especially fine things like those horns and reins, you need to make your design slightly larger than needed so when the laser disintigrates a few hundreds of an inch, the leftover item is the right size.