Johnty – it sounds like you have an interesting Strata Plan what with Owners trading units of entitlement (ref: your other post), but in answer to your post here, as the ceiling of your Lot is merely there to conceal pipework and services to other Lots, both that ceiling and the space between it and the underside of your above neighbour’s floor is Common Property – entirely the responsibility of your Owners Corporation (O/C).
Neither your neighbour nor their plumber may do anything to do with the former’s new shower installation without the prior written consent of your O/C by way of a special resolution at a General Meeting, where >75% of those in attendance must vote in favour in order for your neighbour’s Motion to pass, with that percentage being determined by the units of entitlement (UOE) of those voting and the total UOE of those present and entitled to vote (including proxies).
It is through the procedures of that Meeting where you may express your concerns about the proposal, including those you mention about noise from the shower (if consented) and during the works themselves, and your O/C as a whole can consider other implications such as who will be responsible for the on-going maintenance and repair of the proposed shower (e.g. floor / tiles / waterproof membrane), possible consequences arising from alterations to any common services (e.g. water supply and drainage serving other Lots), and how the O/C may be indemnified from any or indeed all of that (i.e. by a Special By-Law).