The fee to call an extraordinary general meeting should be in the strata management contract. You need to take a look at this document. If it is in the contract, it is legal.
The strata management contract lists how much they charge for their services to the owners corporation. Somewhere in one of the “schedules” at the end of the document, it shows that they charge a certain amount for holding an extraordinary general meeting.
You can get around this. If you have several owners, whose unit entitlements add up to 25% of the total unit entitlements in the strata plan, they can call a meeting. I did it. I called a meeting without involving the strata manager so that we could vote on a few things. The strata manager cannot charge me for something I initiated. However, you have to read the Strata Schemes Management Act 2015 and know something about running a meeting because there are rules about issuing a notice of agenda, voting minutes etc.
What I cannot understand is why the resolution passed in the original meeting did not allow you have ongoing care of different animals. The wording of the motion should have said you can keep zz number of animals for a maximum xx days and include whatever conditions they see fit.
It would be even better to create a by-law to formulate rules around foster care. In that case you might need a lawyer to draft the rules and you would have to pay for another extraordinary general meeting and registration of the by-law.