Precise Logo Vectorization Needed

I have a single-colour, flat PNG logo that must be rebuilt from scratch as a perfectly clean vector. No redesign—just an exact, proportionally accurate recreation in RGB 85-18-12. File expectations ... (Budget: £10 - £20 GBP, Jobs: Adobe Creative Cloud, Adobe Illustrator, Adobe Photoshop, Graphic Design, Illustrator, Logo Design, Photoshop, Vectorization)