maybe im being silly but I have never had a pet before and I have a 9 week old kitten.

since we shut the door with her being on her own in the living room at night when we are in bed, no lights are on - should I be leaving like a small light on for the kitty or are they ok in the dark?

Cats have excellent nightsight, much better than humans so what's dark to you isn't so dark to her. They can even still hunt very effectively at nightime.
She should be fine without a light on, unless it makes her feel less abandoned at night, so there's less contrast to how things are when you're there or when you're not but cats and kittens are generally absolutely fine with the lights off

I've always kept my kittens in the kitchen at night without a light on and they are fine. Cats have very good eyesight.

You are brave leaving a kitten in a living room, overnight.
Mine would have swung from the curtains and blinds, emptied the plant pots, scratched the sofa, and played bowling with everything else he can stick his paws on.