Do I need to have it mapped out with notes on monsters and traps?
I'm not a
DW expert mind, but I've run the game several times with mixed results and have learned from my mistakes. I would say "yes" to notes on monsters and traps, but "no" to a mapped out dungeon.
For monsters, your notes can just be a collection of critters (intelligent or otherwise) you think would be cool to have the PCs interact with. Think a little bit about what kind of dungeon you're going to start the PCs in (Wizard's Tower, Goblin Mine, Cultists' Lair, City Sewer, etc.) and just brainstorm some creatures that could be found there. Then grab 'em from the
DW book (or make up your own) and put their stats and moves on an index card for easy reference during play.
Traps are similar. Think of some cool or classic traps you'd like to see in this dungeon. Write them down on an index card, along with what they do when activated and any telltale signs of their presence. That should all be fiction, though you can note how much damage they do, or write a custom move for the effect. I find it best to
not write down how to get past the trap, as that can blind me to creative solutions the players come up with.
Which is why I say
don't map out the dungeon beforehand. In the games I ran with a fully mapped out dungeon, I found it only stifled my creativity. It was difficult to make hard moves because I knew where everything was and what everything was doing. Sometimes I found myself thinking "Well, there really isn't anything else in this room, but the player just triggered a Discern Realities move. What should I do?" or "Someone just failed a roll, but none of the monsters could possibly get to them. They're all the way over there, behind all these locked doors. Hmm..."
So, in my experience having a "finished" dungeon hurts more than it helps. If you have a cool idea for a certain location (a narrow stone bridge spanning a bottomless chasm, a pillar-lined room with an altar to an evil deity, the stony shore of an underground sea, etc.) write yourself notes cards about that. Maybe include a quick sketch of the area, and notes about who or what might be found there. Then just use those locations when the PCs wander into an appropriate area. It's almost like playing "connect the dots"; you have a couple of set locations you want to showcase, but just make up the places in between them as the players explore.