Poll: Could you do it a bit ____?
- Votes: 423
- Comments: 2
- Added: February 2008
- Polls: 1,170
- Votes: 689,409
- Comments: 4,855
I think in this case the word quicker is an adjective, actually a comparative adjective and as such cannot be used in this context. Correct is more quickly as it is the comparative of quickly, and it indicates manner in which something is done.
E.g. She played golf more skillfully this time.