You can either hit Prestige straight away or go to the Progression tab in the Barracks through the Multiplayer lobby. Think carefully about when you want to do this, as Prestige in Black Ops 6 means you lose access to a lot of the things you will have unlocked.

Black Ops 6 player reaches Prestige 1 without getting a single kill in almost twenty hours' worth of multiplayer matches.

Simply put, yes, your Black Ops 6 Prestige will carry over to Warzone. After its integration with Black Ops 6, Warzone's progression system has received massive changes.