Copper was a 2000 graduate of Washington High School. He finished as the school's career-leader in receptions and receiving yards. He also had 27 touchdowns. He was a three-time all-conference and all-area selection and set season records with 55 receptions in 1997 and 697 receiving yards in 1999. As a freshman, he had 25 catches for 402 yards and three scores. As a sophomore, he set school records with 55 grabs for 1,000 yards, including 4 touchdowns. As a junior, 38 catches for 683 yards and seven touchdowns. In his last year, he registered 41 receptions for 741 yards and 13 touchdowns. He earned honorable-mention All-American honors from USA Today. Copper was also selected to play in the Shrine Bowl and East/West All-Star game his senior season.
College career
Copper accepted a football scholarship from East Carolina University. As a true freshman, he played in 11 games, making 9 receptions for 187 yards, one touchdown and averaged 22.8 yards on 4 kickoff returns. As a sophomore, he started the first 4 games at the H-back position with the departure of Keith Stokes and had David Garrard as the team's quarterback. He collected 13 receptions fot 124 yards, 9 carries for 49 yards, one touchdon and returned 10 punts for 70 yards. As a junior, he started 9 out of 12 games, registering 30 receptions for 395 yards and returned 30 punts for 328 yards. As a senior in 2003, he led Conference USA with 87 receptions. He also had 897 receiving yards, two touchdowns and returned 27 punts for 124 yards. He became the first player in school history to receive All-Conference USA honors. He finished his college career without missing a game, while registering 139 receptions, 1,683 receiving yards, 3 receiving touchdowns, 211 yards on nine kickoff returns, 522 yards on 67 punt returns and 72 rushing yards and one touchdowns on 16 carries. In 2013, he was named to the school's All-Time Offensive Team.
Copper was signed as an undrafted free agent by the Dallas Cowboys after the 2004 NFL Draft on April 30. He was released on September 5 and signed to the practice squad on September 6. He was promoted to the active roster on October 4. As a rookie, he played in 10 games and made seven receptions for 84 yards, but his main contribution came on special teams, where he had 14 tackles and returned 16 kickoffs for 307 yards. In 2005, he appeared in all 16 games, playing primarily on special teams, he totaled 11 special teams tackles and 2 kickoff returns for 32 yards. He was released on September 2, 2006.
On October 29, 2008, he was signed by the Baltimore Ravens after wide receiver Demetrius Williams was placed on the injured reserve list. He appeared in 2 games and was declared inactive in 7 contests.
On March 17, 2009, he signed with the Kansas City Chiefs. He was second on the team with 16 special teams tackles. He was re-signed on March 7, 2010. In the 2011 season, he had a catch drought that started after he had one reception in Week 5 against the Indianapolis Colts and ended in Week 13 against the Chicago Bears. In week 16 against the Oakland Raiders, he played an important role catching three passes for 61 yards. He finished the season with 8 receptions for 114 yards. In 2012, he appeared in 15 games and was placed on the injured reserve list on December 29. He was released on August 25, 2013.