buddy, i live in a similar complex and have been in a similar situation. There are certain requirements that they need to fulfill. For example, as you are the owner, the executive committee have to notify the body corporate company (that is, the managing agents) and they need to, in response notify you of an infringement. Which takes a while. Then, if you choose to, you can ask to call a special general meeting of the body corporate and organise to vote on the issue. Many people will not be able to attend this meeting, so it is best to do as i did and organise to become other owner's proxy votes. Then you can essentially change the charter of the body corporate for your unit (which i assume is under strata title).
Time for the bottom line here. The body corporate has rights, those are to enforce the rules of the block. Those rules do not extend to entering your apartment and removing your property, all they can really do in a situation such as this is issue a fine. Now, as for the argument that you can put forward:
I would suggest that you take to position of the "peaceful enjoyment" article which is present in most body corporates. You can suggest that your posession of these animals affects no one other than yourself, the thinking behind the rule of one domestic animal is that the cat lady might screw up the entire block, or that dogs bark etc.
I have, as the chairperson of the executive of my body corporate, had licenced reptiles (no number limit) added to the pets list for both blocks that i have a unit in.
If worst comes to worst, you could argue that it is part of your business, study or even companion animals (that last one is a little rough, but i've heard it done for multiple dogs with unscrupulous GPs).
Good luck buddy.