I need a vector logo

Type of logo: Emblem, Character
Brand name/slogan in logo: Just Jemima
Ideas for the visual style: retro
Preferred colors: Ice cream style colours (pastel)
Extra notes: I need a girls head - 1950s style, quirky and retro with long blond hair, similar to the attached.
The character can sit on/over a rounded vintage style caravan, surrounded by the business name Just Jemima in a scalloped circle.
Needs to be supplied as a vector with editable elements.

The client has a caravan that is icecream colours......mint green all over with a icecream pink door. Keeping in the style simple and uncluttered so that the logo stands out.

Patternwise, I like scalloped edge, polka dots, though currently prefer the confetti effect.