You may be able to rent a board and paddle from Goodtime (
www.goodtime.com.au/)
As for getting on the water, best that is close to Brisbane for flat water is Wellington Point. Or if on the North side you could head to Sangate or Redcliffe.
If it is surf you are after it is about a 1 hour drive to Currumbin from Brisbane, which has both flat water and surf. For rentals on the Gold Coast you could try Surf FX (07 55313199) or Roar Industries (
www.kitesurfinggoldcoast.com.au) both of which have boards to hire.