Logo re-draw from existing design

My client has designed their own logo in Canva that I need to use on their website.

I need the logo redrawn so that it suitable for web in two formats:

1. As the attached .jpg but 350pxls wide x 100pxls deep - supplied as a .png with a transparent background.
2. A favicon 512pxls x 512pxls - supplied as a .jpg (just the face symbol for this)

For the logo, I need someone to re-draw this exactly as the .jpg supplied, but so that the text "Jo Bailey skin clinic and medical aesthetics" is the same size as the head illustration (so that the text is as equally large as the drawing).

The website is www.jobailey-medicalaesthetics.co.uk and you can see the .jpg placed there for context.