Yes, you have to make your way though part of the dungeon again. But this time when you get back up to the first floor, rather than fall down the hole to get the floater, go behind the room with the holes and there is a staircase that takes you outside.

I made the mistake of taking the staircase once before dropping down and getting the floater and had to go back to town to stock up and do the whole cave again. Arrghhh!!. I never made that mistake again.