The following script seems to work properly under Mac OS X 10.7.3:
set nextTime to ((current date) + 60)
tell application "System Preferences"
reveal anchor "Schedule" of pane id "com.apple.preference.energysaver"
tell application "System Events"
tell sheet 1 of window 1 of process "System Preferences"
if value of checkbox 1 = 0 then click checkbox 1 -- Start up or wake
click pop up button 2
click menu item 3 of menu 1 of pop up button 2 -- Every Day
set value of UI element 10 to nextTime
click button "OK"
I haven't tested this, so it may take some tweaking (I'm suspicious of the 'quoted form of' bits, because I don't know if pmset requires double quotes), but it should work. basically it tells the power management system (pmset) to schedule a one-time shutdown in 1 minute and a one-time poweron in 2 minutes.
set shutdownTime to do shell script "date -v+1M '+%D %T'"
set restartTime to do shell script "date -v+2M '+%D %T'"
do shell script "pmset schedule shutdown " & quoted form of shutdownTime
do shell script "pmset schedule poweron " & quoted form of restartTime
If you have troubles it's almost certainly a matter of quoting. it might be easier in that case just to rewrite it as a plain shell script.
See man date. You can use -v+#S to specify seconds (e.g., -v+20S for 20 seconds), but keep in mind that there are sometimes non-negligible times involved, and I don't know what will happen if you try to schedule a shutdown or restart for a time that's already passed. you could probably set shutdownTime to as little as 1 second in the future, but you'll need to account for the time it takes to finish shutdown in restartTime.