The form states that they (SW) should be informed of any change of circumstances that would affect her Carer's Allowance so I would do just that.
Write a note (keep copy) quoting her refs. stating your new situation, the date you started your new job and enclosing proof of income.
I can't see any reason for a new application since she is already in receipt of the Allowance. The adjustment should then be made,eventually!!!!!!!