I would like to take leave from September 24 to 28, 2012. Can you arrange for Shing to cover my desk during that time period?
I would like to take leave from 24–28 September, 2012. Can you (please) arrange for Shing to cover for me during that (time) period?
I don't know your relationship with the person you're writing to so whether you say "please" or not is up to you. I would write the date a little differently, as I've shown, and I feel that "time" is optional.
The main change is to the more natural "cover for me", I haven't heard "cover my desk" but of course it may be a common way to express this in your situation, so that again is your decision.
not a teacher
Student or Learner