You can enable timestamping at Options (Alt+O) : IRC : Messages : "Timestamp events".
You may also modify the timestamp format here. To see a list of all the possible time/date parameters, type in any mIRC window "/help Time and Date Identifiers". Two examples: [HH:nn:ss] or -hh:nn tt-
If you now don't see new messages prefixed with a timestamap: right-click the respective channels/windows in the treebar/switchbar and set "Timestamp" to "Default" or "On". In case you still don't see any timestamps, you're using a script that replaces the "default" display of messages (ignoring all the settings mentioned above).