Cooper reportedly moved into his $880,000 home in Bulimba.
The couple are believed to have always intended to keep their split under wraps until after Christmas.
Cooper could not be reached for comment on the separation.
He is staying with his family in New Zealand for the holiday break.
He has been sharing his experiences of home online since he landed in the country on Christmas Eve.
He spent Christmas with his family in his hometown of Tokoroa before heading up to Kaikohe on Boxing Day to catch up with more relatives.
"Today at my Lil cuzies house I took his motor bike for a spin ;) I know what I want next Christmas :)" he said on Twitter that day.
The next day, Cooper said his grandmother had shown him all the mail fans had sent her.
"One young girl send a photo of me an her & her pet lamb named quade. Top support :)"
He also posted a picture of himself having a "nice relaxing dip" in hot springs in Northland. "Damn they stink but feel sooo good!"