Civoniceva won the Brisbane club's coveted "Player of the Year" award in 2004. Civoniceva was selected in the Australian team to compete in the end of season 2004 Rugby League Tri-Nations tournament. In the final game against Great Britain he played prop forward in the Kangaroos' 44–4 victory. He was the 2006 Brisbane Broncos season's player of the year and he played at prop in the Broncos' 2006 NRL Grand Final victory. As 2006 NRL Premiers, the Brisbane Broncos travelled to England to face 2006 Super League champions, St Helens R.F.C. in the 2007 World Club Challenge. Civoniceva played as a prop forward in the Broncos' 14–18 loss against St Helens,