Time Turners can't go back that far.
J.K. Rowling has said that it's impossible for those 1-hour Time-Turners to go back farther than 5 hours. (See quote below.) So: She can't.
If you're asking about making sure he doesn't come back, how would she do that? She can't do anything that would prevent him from coming back, as she doesn't have the power to be anywhere that it would make a difference.
As our investigations currently stand, the longest period that may be relived without the possibility of serious harm to the traveller or to time itself is around five hours. We have been able to encase single Hour-Reversal Charms, which are unstable and benefit from containment, in small, enchanted hour-glasses that may be worn around a witch or wizard’s neck and revolved according to the number of hours the user wishes to relive.
Now, there was a Time-Turner that could go back years, but they didn't know that existed until the time of The Cursed Child.
J.K.R. has also commented on the issue of traveling back in time to change things:
Also from Pottermore, same article
I went far too light-heartedly into the subject of time travel in Harry Potter and the Prisoner of Azkaban. While I do not regret it (Prisoner of Azkaban is one of my favourite books in the series), it opened up a vast number of problems for me, because after all, if wizards could go back and undo problems, where were my future plots?
I solved the problem to my own satisfaction in stages. Firstly, I had Dumbledore and Hermione emphasise how dangerous it would be to be seen in the past, to remind the reader that there might be unforeseen and dangerous consequences as well as solutions in time travel. Secondly, I had Hermione give back the only Time-Turner ever to enter Hogwarts. Thirdly, I smashed all remaining Time-Turners during the battle in the Department of Mysteries, removing the possibility of reliving even short periods in the future.
And I'm sure that everyone is familiar with How Harry Potter Should Have Ended, which is basically this scenario...