I need to have the phone number, email and the website to add them in the business card

It is unclear from the brief what information and contact details should be included. Do You really want single -sided card as it specified in brief?

In relation to details to go on the card, preferably 2 sided so appointments can be written on the back

DSD logo on LHS
Smile background RHS with DR Institute name over the top of the picture
I prefer darker colors in the professional elegant style
address: Level 1
233 Collins St. Melbourne 3000 Australia
1800 386038