Bhavani Prasad,
I just came out of the same problem.
As you rightly said, "Quick Entry" and "Suggestions" are derived from the Worklist configuration of your data entry profile.
When you use these two options, you will not have an option to change any of the cost objects (including AWART). Only field you can change is hours.
Now the solution for you is to make your worklist filed selection configuration same as data entry screen field selection configuration.
Thanks
Krishna