The Kings made the moves Monday before their game at Vancouver.
Carter hasn't played since Oct. 30, missing 10 games with a foot injury.
He was the Western Conference's top goal-scorer last season. He has five goals and four assists in 14 games this season.
Quick's groin injury is expected to keep him out until late December. The 2012 Conn Smythe Trophy winner hasn't played since Nov. 12, missing the Kings' last six games.
Ben Scrivens has been one of the NHL's best goalies in Quick's absence. Los Angeles is 4-0-2 in his six starts since Quick's injury, with Scrivens allowing just seven goals and posting two shutouts.