the Witch made it too difficult on herself

The problem is there are two variants to the prophecy:

"...down at Cair Paravel there are four thrones and it's a saying in Narnia time out of mind that when two Sons of Adam and two Daughters of Eve sit on those four thrones, then it will be the end only of the White Witch's reign but of her life..."


"When Adam's flesh and Adam's bone,
Sits at Cair Paravel in throne,
The evil time will be over and done."

For the second version, Peter could still fulfil the prophecy if the witch killed Edmund so she used Edmund to attempt to get the rest of them.

I am not certain about the two variants, but it was said it would likely delay the prophecy longer if she just went ahead and killed him if it could still be fufilled.