Moving the wastes in a slab will be the costly part. Accessing water through the walls is not that hard but the disposal of the waste water into the sewer will be. You can usually get a sewer plan for your block from the water authority or Council. This will show you where the sewer is in relation to your garage for that option (which may be the best option depending on sewer). Internally I’d allow $1500 per metre in labour that the slab has to be jackhammered for the new piping plus the costs of fixtures and materials. Impossible to indicate the external costs without knowing where the sewer is. Don’t forget to allow for the new flooring, cabinetry and wall rectification. And you’ll need to check with Council to see if a permit and plans are required. Maybe be a better option to build custom cabinetry into the storage space and use it for kitchen over flow.

I would look to move the laundry under the stairs first and then the garage, check out the following https://www.saniflo.com.au/14-installing-a-kitchen-or-laundry-room

good luck

The enclosed storage space is showing it is 1000mm deep. This might not be enough room to have a front loader and swing the washing machine door open and closed. Same with a dryer. Top loader washing machine will be fine. At the moment with Euro laundry this doesn’t matter as the space is not enclosed. Unless you are going to knock the store room wall down, I don’t think it is practical to put a front loader/dryer in that space.

Also, is this a stand alone dwelling or does the garage wall and full right hand length of the home connect with another home? You will be compromised in any decision if it is connected to another dwelling.

Siriuskey suggestion for Saniflo may be the only alternative. After you have carefully measured spaces for usage.

A Euro Laundry is a Laundry in a cupboard which means the door/s to the cupboard would be open when using the washer and dryer, so I don't see a problem

If the washer and dryer are front loading and placed in the store area which is 1000mm deep the doors on the appliances may not open because it is an enclosed room not a cupboard. Yes they are currently in a cupboard in the kitchen. Only option is to put them right in the front of the opening door.

And then you shimmy past them to store other household items.

Thaks for the feedback lots to think abouy and not an easy solution by the looks if things

Moving it to the stair cupboard shouldn’t be hard and since washing machines pump their water out it could still remain connected at current points. Get a plumber in to quote and confirm.
It might be more cost effective just to fit the storeroom out effectively. As it is next to kitchen it could be your pantry.

You said you are “looking” at the home, so with that I assume you don’t live there. But another question, are the internal walls brick or stud walls?

If the internal wall of the storage room is a simple non-bearing stud wall, you could remove and put laundry and storage behind bifold doors, or similar doors to kitchen. The access to Australian standard plumbing is the big question.