Once you defeat her, Geralt will burn the notes. It's not the most fleshed out ending, but it does give you an additional boss battle. Plus, Keira dying in combat is better than her getting executed and her corpse put on display.

What happens if I don't kill Keira Metz?

As long as you convince her to go to Kaer Morhen, with or without her notes. If not, you either fight her ( kill her ) or she'll get impaled by Radovid later in the game, thus, wont be helping for the fight against the Wild Hunt.

What should you do with Keira?

Swim to Fyke Island from your evening with Keira. Head to the tower to find Keira. She found what she was looking for—notes that could create a cure for a plague. She plans to sell it to King Radovid for money and protection.