The Draconid shower, also known as the Giacobinids, is unusual because it appears highest in the sky when it gets dark.
On the night of October 8 until early morning of October 9, the Draconid meteor shower will not be affected by the 23% illuminated waning crescent moon.
The last quarter moon will happen at 13:48 UTC on October 6. In 2023, we can see a small moon on October 8 and 9. It won't cause any problems for the shower.
On a moonless night, you could see around 10 Draconid meteors every hour.
predicted* for October 9, 2023, at 7 UTC. Highest in the sky in the evening hours. See chart above.