The body corporate can’t stop people from having pets

Not correct. Refusal to approval can be lawful in some rare circumstances, but a body corporate cannot refuse consent just because a pet may do something. If a pet does breach the by-laws later, or the reasonable conditions of approval, then an order can be sought for its removal based on the by-laws being breached. But a blanket refusal to the keeping of pets is almost always going to be unlawful.