For this logo, I've kept it welcoming and friendly, something that is clean and professional yet open to all sorts of doctors regardless of age or background. Basically saying "We're so glad you're here, let us help you learn more!"
I think this minimal and modern logo will be the perfect fit for the brand!

Because of its simplicity and curves, it would print great on all sorts of materials and you will not lose any detail.

The blue I used has a great contrast with white, which is the background of the client's website. So, It'll fit perfectly!

The symbol is made of a plus sign that shows the medical aspect of your business, a smiley face in the center to show a welcoming and educational environment, and finally a pedal shape as the background to give the whole thing balance and contrast, it could also be seen as an arrow going from bottom to top.