#1 — both will do, but they'd yield different meanings.
To do something differently means to do it in another way.
For exaple: Hey, that's the right answer but you can solve it differenty, in just three lines!
To do something different is... well I suppose you've got it. I means doing another thing.
For example: You've been sitting in fron the TV all day. You better do something different, go make a stroll!