Taking City of Sydney (the council with the most strata schemes) as an example, their website and forms require “verified consent from all of the registered owners” before a DA can be submitted.
Now, the Owners Corp is not the registered owner so it seems like there may even have to be a unanimous agreement for a change of use DA (although I could be wrong) but, at the very least a special resolution.
Also, Note 6c on the City of Sydney DA form says an application for a DA from a strata scheme must be accompanied by a “copy of resolution or minutes showing that a special resolution has been passed at a general meeting of the owners corporation that specifically authorises the change to common property.”
Any change of use would have an impact on common property so, again, at the very least a special resolution would be required.
Also, I suspect you would have to change your by-laws to accommodate short-term letting, so there is another special resolution requirement.
I would say that if your secretary puts this motion to a meeting and it isn’t as a special resolution you should move to have the motion removed from the agenda as it is incompetent and a breach of strata law.
A smart EC would get some legal advice before pursuing this.
Other councils may have other rules but they tend to be standard and governed by the Local Government Act.