Note what I said - if the operator is the organisation wishing to move the animals then no AOC is required.
jxc has not been entirely clear in this, but it certainly looks like it is jxc's hypothetical customer that wishes that the animals be moved, and jxc is asking about an operator willing to buy them and so move them in compliance with the customer's wishes. As flynowpaylater implies this used to be a well-known loophole, but it is now closed, so that operator would require an AOC.
Pace - in the case you are describing the valuable consideration is independent of the flight. The customer would be willing to pay for the product without any flight being involved if he could be assured it was manufactured to specification. The flight is a convenient means of meeting at a suitable location for the manufacturer to assure the customer of this, it is not inherent in the product.
If I read it correctly jxc is looking to supply a product to a customer in one location that is currently in another location, and the only value added is in transport - therefore the valuable consideration (i.e. profit) to the hypothetical operator is for the transport, therefore that is a commercial air transport flight. If this is a retail sale, or a wholesale distribution network that needs to move stock for general sale in the normal run of its business, then that is a different matter.
The difference, I suspect, will come down to whether a price was agreed for the customer to buy off the operator before the operator bought the stock, which implies a flight for the customer not the operator, and who sourced the animals, arranged checks on their health and quality and negotiated the price at source. If the operator did all that and bought the stock before selling it then they would have a good case to be a wholesale or retail organisation simply moving their own stock. That is the case CJ driver is talking about.
Advice to jxc: ask the CAA, and be very specific (and truthful) about the business plan. If they have any doubts then get specialist legal advice.
If you fly illegal charters you will eventually be prosecuted. Initial fines are pathetically low, but they do rise if you fly illegally again so you are out of business at that point, hopefully stuck in the back end of nowhere with an aircraft SAFA inspectors will not let you fly. Then it makes it very, very hard to operate legally afterwards - the CAA will be very wary of you.
If you have an accident on an illegal charter (and it is surprising how many accident flights both private and commercial are illegal for some reason; paperwork may not help you fly, but lack of it seems to signal lack of safety culture) you will not be insured, and it will cost you a very large sum of money, usually life-changing, bankrupting amounts of money. You will also be arrested, charged with many offences, and I hope gaoled.