Following are some answers from a purely legal, rather than ethical perspective. I am not in WA but this is from the WA legislation, BC = body corp or strata council :
A BC cannot reasonably refuse a consent to carry out works on common property by the proprietor if a lot.
Firstly have you received notification in writing. The notification must outline the reasons for their refusal, including the information relied upon for making their decision. It may also be worthwhile to write to the BC for an explanation regarding why other title owners have AC's installed and you are not allowed. Their justifications must align with both the Strata Titles Act and the by-laws of the specific BC. This alignment needs to be in relation to the outline of goals and intentions of the BC.
If they refuse at first instance, the BC may have an inbuilt appeal process. If it does find out the process and follow it.
Subsequent to that the appeal is the State Administrative Tribunal (SAT).
The SAT has the power under S 85 to:
Order with respect to certain consents affecting common property
Where, pursuant to an application by a proprietor for an order under this section, the State Administrative Tribunal considers that the strata company for the scheme to which the application relates has unreasonably refused to consent to a proposal by that proprietor —
(a) to effect alterations to the common property; or
(b) to have carried out repairs to any damage to the common property or any other property of the strata company,
it may make an order that the strata company consent to the proposal.
Also they can not levy the costs against your lot should you lose.
S 111 Expenses of strata company on appeal
(1) Notwithstanding section 36, where the strata company is the respondent to a successful appeal to the Supreme Court from the State Administrative Tribunal by the proprietor of a lot, the strata company may not levy in respect of that lot a contribution towards the expenses of the strata company in relation to the appeal.
RATHER THEN JUST GO AHEAD AND INSTALL IT
Another option would be that, if you install a split system airconditioner that has a standard 10A plug on it, rather than a hardwired switch. You could argue for that this is furniture rather than a fixture. This is then comparable to where you put a bolt or hook in a wall to hang a pot plant or picture. It also compares to you buying a portable airconditioner and placing some bolts in the wall to attach it to. You are then not making a permanent connection to the electrical supply of the building and the unit is easily removable and any holes could be patched and rendered over. If you wanted to go this way you should give them notice of your written intention to do so, 14 days prior to the installation. They would then have this time to either give or not give their consent. If consent is not given, then again they have to outline their grounds and make sure that they have not unreasonably denied consent.
If either action results in a denial of consent, you could then write to the BC stating that you believe that the grounds for denial of consent are unreasonable and you wish to challenge it. State in your letter that you do not wish to cause any harm to your relationship with the BC you just want to make sure that the decision is complying with the law. As it is your firm belief that the denial of consent does not comply, further, that you have already waited 6 months for the upgrade they are waiting on, you retain your right to make an application to the SAT.
Going to the SAT should not incur legal fees on your behalf or theirs and should be relatively cheap if it is the same as the QLD situation.
All of above does not constitute advice, it is for general information only. See a lawyer or do your own investigations.
