I did a quick Google search on this and found an article written by me (which was gratifying, if nothing else). This is what it says:
In Queensland the committee can also vote on issues without formally holding a meeting. There a “flying minute” is used, for instance, when urgent work needs to be approved in a hurry.
According to this document, “decisions may be made in this manner if all committee members are given written notice of the motion and a majority of the voting members of the committee gives written agreement to the motion.
“The notice (or the ensuing committee member’s agreement) does not need to be in writing and can be given orally or by some other form of communication. Any motion voted on under these provisions must be confirmed at the next committee meeting.”
So what you have probably come up against here is a combination of infrequent committee meetings and a strata manager who charges on a per-use basis, rather than a flat fee.
If you want a decision on your cat before the next EC meeting, which could be months away, this is extra work for the strata manager and he is going to charge you for that. Otherwise, I would assume, your committee will just say wait until the next EC meeting.
So find out when the next EC meeting is and decide if you can wait that long. There should be no charge if your request is part of a meeting that would happen anyway.