As an owner you are entitled to see all documents relating to the owners corporation and unless this was agreed in advance to be a secret ballot, you can see the votes.
I would immediately seek mediation at Fair Trading, as a precursor to action at NCAT against the strata manager.
As far as the committee dragging their heels, Section 232 (2) of the Act sets a limit of two months after which non-response will be taken to be a refusal by the committee to fulfill their duties. That, or a straight rejection, can then be challenged at the Tribunal.