If you are lucky enough to not be running on Vista(*) the "AT" command might be of use to you, with this it would be possible to issue the command you describe in your question at 1am.
Then you would schedule a second command using "AT" at 2am to use the "TASKKILL" command to stop the process, if you are happy to have the command terminated with prejudice.
Failing this, write a tiny program which stays resident in memory and executes both the 'start' and 'stop' instructions when it determines it's the correct time to do either.
(*) I've experimented with AT on Vista and it doesn't seem to work for me, your mileage may vary. The task scheduler also seems equally as suspect.