In terms of "is there much that unlocks after level 6," the answer is definitely yes. There's some stuff that unlocks all the way to level... I think 10 or so, in terms of the macrogame.
In terms of the actual monsters, there's new stuff unlocking up to level 12 at the moment, I think.
In terms of region types, the last region to unlock at the moment is the swamp, at region level 60. But there are others in the 20s and 30s and such, too.
In terms of crafting materials, at the moment there is stuff that unlocks all the way to level 70 (coral), although coral doesn't yet have anything that you can craft from it because I figured I have time.
That's just speaking to what is in the game now, not what will ultimately be in the game, of course. Most things will unlock before level 80 or so I expect, so that "playing the full game" can mostly be done prior to level 80. But as you go higher, and we add more stuff, you'll be getting the new stuff at the higher levels. If your first time getting ice cross was at level 100, for instance, it would still be as awesome then as if you got it first at level 1, like now.
And I'm sure we will make a few things for much higher than level 80, just to reward the...
insane dedicated.