I’m ASSUMING they cannot just use their larger percentage to vote for a benefit for themselves.
Why would you assume that? Decisions made by committees and at general meetings can be challenged at NCAT, or even in court if they are seen to disadvantage a minority of owners. But there’s no law specifically against it.
But there’s certainly nothing about pets being allowed on common property.
The key is if there’s nothing saying they can’t. Your fall-back is the part of strata law that deals with dogs that have permission but turn out to be a nuisance. Oh, and make sure your lawyer is a strata expert otherwise they may be no more clued-up on this stuff than you are.