Not so hasty, flynowpaylater. If jxc's employers are in the pet sales business, and choose to operate their own aircraft to transport their own inventory, then they do not need an AOC. It is no different to a company owning an aircraft to transport their own executives.
If however "Pets R Us" charters an aircraft from someone else to transport their inventory, then the supplier of the aircraft WILL need an AOC.
Flaymy was therefore right in the first response - if the company/person operating the aircraft and the company/person shifting the animals is the same, then no AOC is required.