The article also says that she was caught on CCTV leaving and entering the house multiple times. Even if she left the body there, eliminating the need for her to make multiple “drop off” runs, she’d still be the last person seen entering the house and subsequent DNA evidence would be enough to convict.
The taxi driver reporting her to police just expedited how quickly she was caught. The crime would have likely been discovered as soon as the teacher failed to report in to work or to her next appointment. But if she hadn’t been reported so quickly, it would have given her more time to disappear.