If an original architectural design is made, then the designer will own the copyright in those designs. If the designer is the architect, then the architect will own the designs. If you are building a new house, then you should ask the architect to assign his or her copyright in the designs to you.
If someone copies the architectural design, then you can sue them for copyright infringement under section 115 of the Copyright Act 1968.
A court can grant an injunction, and either order damages (to compensate you for the diminished value of your house) and additional damages for flagrant infringement, or an account of the infringer's profits.
In the case of Coles v Breden, Clark and Dormer (No 2)  QSC 28, Stephen Coles was awarded $70,000 in damages and his legal costs, in addition for orders for Dormer (and other infringers) to stop copying Coles' house design.
The background to this story is that an architect called Mr Skyring design a particularly distinctive house design for Mr and Mrs Spicer. The Spicers put the house up for sale and two two bidders battled it out for ownership - Stephen Coles and the Bredens.
Coles got the house, but the Bredens got revenge by buying a lot of land three blocks down and rebuilding the same design using the Spicer's builders.
Coles got an assignment of the copyright rights from the architect Skyring and got his lawyer to send a cease and desist notice to the Bredens. He argued the infringing copy made his home less distinctive, and hence it would decrease its value.
Nevertheless, the Bredens continued to copy the house design. Accordingly, Coles sued the Bredens.
The Bredens argued that the Spicers were joint owners of the design, so the Coles didn't completely own the copyright. They also argued that they started making their own building plans before the architect Skyring assigned his copyright to Coles. They also argued that they did not make an exact copy of the house design.
The judge found in favour of Coles. The judge held that the Spicers' initial design ideas and Skyring's building plans were two separate works, and the Spicers' tweaks to Skyring's design were insufficient to give the Spicer's joint author rights.
The judge found the Bredens had made a "substantial" copy of the house design. He said:
"The elements of similarity are not merely found in the repeated coincidence of the lineal and spatial forms on the plans but also in identical notations upon the plans. In one instance identified by Mr Gleeson an error in the Skyring house plans about window height was replicated in the Breden house plans. In another a reference to the location of a bathroom window in the Skyring house plans was replicated in the Breden house plans notwithstanding that a variation in the layout of the Breden house, necessitated by the nature of the block, meant the window should have been on the opposite side. In short it is obvious copying on a substantial scale must have occurred "
The judge ordered the Bredens to change their house design so that it was not a substantial reproduction of Coles' design.