You have two options. You can build the table in the new sheet programmatically, or you can select and copy the table(s) from the first sheet and copy it(them) in the new sheet. Here is code for the second option. Having not seen a screen grab of your template sheet, you may have to adjust, but this should give you everything you need. If you run into complications, please post a screenshot and description of your template sheet. Updated to account for a crazy number of tables in the sheet. Updated again to demonstrate how to change the active sheet.
tell application "Numbers"
activate
tell document 1
set tempSheet to first sheet whose name is "My Template"
set active sheet to tempSheet
tell application "System Events"
-- deselect all
keystroke "a" using {command down, shift down}
delay 0.1
-- select all containers (tables, text items, etc.)
keystroke "a" using {command down}
delay 0.1
-- copy the containers
keystroke "c" using {command down}
end tell
delay 0.1
set dateString to (month of (current date)) & (day of (current date)) as string
set thisSheet to make new sheet with properties {name:dateString}
tell thisSheet
delete every table
tell application "System Events"
keystroke "v" using {command down}
end tell
end tell
end tell
end tell