Jack, I think your right. It is unlikely that the first cox ride on was on the market when the photo was taken, given the lack of signage on the matter. Is the dating of the photo correct? I think it is. A quick google search informs me channel nine first broadcast in Brisbane in August 1959. ( I'm looking at the TV antenna and the TV sign on the shop.) The only other obvious 'dater' of the photo are the cars, and are unhelpful being all from the fifties.
Perhaps the Owen Cox & co name has lived on outside of family control as the cox industries business has.
Cheers,