Mark, I think you over generalise about Gen Y, but that's another discussion
However, I understand your concerns about 'pet leave' becoming a problem. It really needs to be clarified in the FWA.
There's an easy way to stop this example being exploited by all sundry as a precedent. Ask the individual to get a short letter from the vet explaining what's wrong with the animal and why, in the opinion of the vet, the animal requires constant attention.
In my experience vets tend to be no-nonsense, pragmatic people who would be unlikely to provide such a letter in a case that was not genuine.
As for the cost. I wasn't disputing the fact that there is a cost in the case of the individual, but because this particular leave is deemed to be discretionary and not an automatic entitlement for all staff, then the cost doesn't have to be applied to every staff member.
Notwithstanding the arguments so far, the more I think about this the more I think it
should be taken as annual leave.