the easiest way is to use the shell, zip rename and move can be accomplished at the same time
property backupFolder : "Server HD/Library/Filemaker Server/Data/Backup/"
set dailyFolder to backupFolder & "Daily"
set dailyZippedFolder to backupFolder & "Daily Zipped/"
set timeStamp to do shell script "/bin/date +%Y_%m_%d"
set ZIPfile to quoted form of (dailyZippedFolder & timeStamp & ".zip")
do shell script "/usr/bin/zip -jr " & ZIPfile & space & quoted form of dailyFolder
do shell script "/bin/rm -rf " & quoted form of dailyFolder & "/*"
zip warning: name not matched: Server HD/Library/Filemaker Server/Data/Backup/Daily
zip error: Nothing to do! (try: zip -jr Server HD/Library/Filemaker Server/Data/Backup/Daily Zipped/2014_07_05.zip . -i Server HD/Library/Filemaker Server/Data/Backup/Daily)
If Server HD is the startup volume the path is "/Library/Filemaker Server/Data/Backup/
If Server HD is an external or shared volume the path is "/Volumes/Server HD/Library/Filemaker Server/Data/Backup/