The Kings made the moves Monday before their 3-2 come-from-behind overtime win against Vancouver.
Carter hadn't played since Oct. 30, missing 10 games with a foot injury, but managed to record an assist in 15:48 of ice time.
He was the Western Conference's top goal-scorer last season. He entered Monday with five goals and four assists over 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' past six games.
Ben Scrivens has been one of the NHL's best goalies in Quick's absence. Los Angeles is 5-0-2 in his seven starts since Quick's injury, with Scrivens allowing just nine goals and posting two shutouts.
Information from The Associated Press was used in this report.