Run Dominions from the command line (or edit the target in a shortcut) using "dom.exe -ddd". The number of d's determine how much gets written to the log file, which is a normal text file that will appear in your Dominions folder.
yup. once you've started dom3 with debugger, go straight to the game of interest and watch the battle. quit game and your debug log with just that battle will be created.