Like others have said, you don't trade a Doughty unless he wants out. This team can still contend with a Doughty patrolling the blueline. They just need to make better decisions in player personnel, but there's no reason why this team can't bounce back.
Look at how long it took the Penguins to get back on top, and how many years of trade rumors they had to deal with involving Malkin's name. Looks like they didn't have to trade him in order to win the Cup again.
They made a big trade for a forward in Kessel and didn't give up much to obtain him, and their biggest contributors outside of their core were from a bunch of young players they injected into the lineup, and role players like Bonino and Daley who were able to elevate their play.
Sure, there should be concern as players like Kopitar, Carter, Brown, Gaborik all age and still consume a healthy amount of cap space, but at least two of those players can still contribute a good amount of offense. They need to do a better job at drafting and developing talent that could support them, like they did with Toffoli and Pearson. They'll need more out of Kempe and Brodzinski, Shore and/or Dowd have to step up and prove themselves. If they can't, they're going to have to look elsewhere for players who can succeed in their roles.
The new management group does have to make some shrewd moves, but this can be fixed, and Doughty is a central figure in getting this team back on top. Now many teams can boast having a defense led by a defenseman of his caliber. You trade a Doughty, then you're going to have to wait for a very long time to find a suitable replacement. Look how long it took for the Kings to replace Blake after trading him in 2001. They had to wait until 2008 when they were fortunate enough to have the 2nd overall selection in one of the deepest drafts in league history.
Before Blake, their best defenseman was Larry Murphy, and they traded him for crap while he was still in his early 20s. This team has only had two defensemen capture the Norris, Rob Blake in 1998 and Drew Doughty in 2016. You only move Doughty if he wants out, and if you move Doughty, you might as well look at trading anyone over 30, and good look doing that with the NTC/NMC that these players have in their contracts.