No need for carbon dating, just a DNA test on the wood..It will be easy to prove.
Using the suggested 40000 animals, let say on average they do 2 ounces of poo per day each, thats 80000 ounces or about 2 and a quarter tons of poo per day in the bottom of that "ark".
Don't know how anyone could get rid of that much poo on a daily basis for a year but it surely would have soaked into the wood. Test the wood for poo, if you can find poo from any animal other than something that is or was local (platypus, alpaca ?), I will open my eyes a bit wider.
Whole place would have smelt like a two-hole toilet in the outback.
Suggest the only poo they will find, will be from the well known Bull.
Plus, the statement that the wood is in great condition, would mean that lots and lots and lots and lots of hair will still be there. Possibly another DNA test subject.