I wouldn't lend my SLR to anyone, family or not. I wouldn't want to run the risk of ruining a relationship if the camera comes back spoilt. Heck, I wouldn't even let my wife touch my camera.
My colleague once lent his camera to his brother-in-law, and the camera came back badly dented (I saw the damage and it wasn't trivial). The bro-in-law just acted blur.
Your cousin recognises that it is not a small investment (otherwise she would have bought her own SLR), so I don't see any reason why you can't refuse her. Remember, it's your camera, so it's your choice.