Not necessarily a "quest", but a simple page saying what the "pick a realm" screen means etc, explaining that new chars are encouraged to join a warring realm with a lot of action, so that they can quickly get their feet wet, because a warring realm is likely to also be a fairly active one, meaning they can talk to some people in game etc. This alone will give new players a good sense of what to do in the game, rather than just joining a realm based on the cool name.
In the case of new players, there could also be an "are you sure" pop up if they choose a slower, less active realm, saying that there game play may be slower and more boring if they start there. Not to turn newbies off certain realms, but for a first time player its rather important, for someone just creating a new char they wouldn't need to worry abut the pop up, or you could remove it for already established players.
This will also give some of the slower realms that never war, a little bit of incentive, because if warring realms are more likely to get the new chars, then they will have to start something to get some newbies.
Also I feel that new players are more likely to go from a warring realm to a slower realm if that's what they prefer, rather than start off in a slow realm and just feel bored and quit. Its a sad truth but its a truth none the less. For an already slow game, joining a slow realm where they feel there is nothing to do can instantly turn a player off.