Logo Conversion to DWG & HD

I have my logo in a clear PNG/JPG and need it rebuilt as a true vector so that every curve and line is identical to the original. The primary file I’m after is a clean DWG that I can drop straight into CAD and laser-cut software, but I also want high-resolution exports for merchandise... (Budget: $10 - $30 AUD, Jobs: AutoCAD, CAD/CAM, Graphic Design, Illustrator, Logo Design, PDF, SVG, Vector Design)