[DerekM]

This should do what you want assuming your due and done column are date types. If you're using rich text you'll need to change the comparison.

*ooops forgot to check the due column for a value, fixed*

tell application "OmniOutliner Professional"
tell front document
repeat with theRow in every row
-- change "done" to the name of your done column
set theDate to value of cell "done" of theRow
if theDate is missing value then
if (value of cell "due" of theRow is not missing value) then
set value of cell "done" of theRow to "today"
-- change "due" to the name of the due column
set value of cell "due" of theRow to missing value
end if
end if
end repeat
end tell
end tell