Career
He also represented the Serbian national basketball team internationally. Paunić began playing basketball at a professional level in the Adriatic League when he was a teenager, beginning with Serbian club Partizan in the 2004-2005 season. He spent next season on loan at Mega Ishrana and Mornar.
In 2006 he was sent to Vojvodina Srbijagas as part of transfer in exchange for Milenko Tepić.
He spent two seasons in Vojvodina, and then in 2008 went to Oostende. In December 2009 he goes to Greece and signed with Aris Thessaloniki.
In August 2010, Paunić signed with the Russian team British Columbia Nizhny Novgorod where he stay till April 2012, when he moved to Italy and signed with Virtus Bolgna for the rest of the season. In July 2012, Paunić signed with the Ukrainian side Azovmash.
He left them in December 2012.
Couple days later he signed with Lagun Aro GBC till the end of the season. On September 25, 2013, he signed a one-year deal with Baloncesto Fuenlabrada. On October 30, 2014, he signed with Astana in Kazakhstan.
On December 18, 2014, he left Astana and signed with Budućnost Podgorica for the rest of the season.
On August 25, 2015, he returned to Baloncesto Fuenlabrada. He played at the 2010 International Basketball Federation World Championship in Turkey where Serbia was fourth, and at the EuroBasket 2011 in Lithuania where Serbia finished eight of 24 teams.
