Adding custom mesg. when redirecting "exec 2>stderr.err" ?

Doubt regarding using "exec" command to redirect the STDERR to a file. e.g I did it this way.

mystage.sh

#!/bin/sh exec 2>stage.err
....

....

cat stage.err
mv: cannot move `/root/stage' to a subdirectory of itself, `/root/stage_old/stage'
ls: *.zDB: No such file or directory

................
Now I want to add some timestamp details and some line indetations for this error log along with the redirection.
How should I do that ? Is there any method for that ?

Can you help me out. I want the error file to be as below

cat stage.err

Timestamp :30-06-08-01:39:10

mv: cannot move `/root/stage' to a subdirectory of itself, `/root/stage_old/stage'


Timestamp :30-06-08-01:39:12

ls: *.DB: No such file or directory

Kindly help me in this regard !!!

Thanks
Shankar