Try a backlit setting maybe? It flashes, but the shutter opens later, so it usually helps cut back on red eye and wash-out-ness. But like not using a flash, you'll have to hold it very still. My mom has the same issue with her Nikon (blurry pics). I'm hoping to play around with it more on Christmas and see what the deal is (I've only used Canons) b/c I want to switch to Nikon.
One thing that comes to mind is her furr. I have a blurring problem a lot with Beckham because he is solid gray. If he's in the center of the photo, and most cameras look to the center to auto-focus, the camera doesn't know what to do b/c there is no detail. I see your kitty is the same, the torti markings are not detailed enough for a camera to pick up on. I'm not sure how the Nikons work, but my camera gives me a little box in the center that indicates where it's going to focus from and if I point that at Beckhams eyes, nose, or the edge of his body to focus (hold button down halfway), then move the camera so he's now centered, and shoot the pic, I get better results. Posh is easier for the camera because she is black and white with more striking eyes.
Other than this, I mainly use completely manual settings for indoor shots, unless the cats are by a window and there's enough sunlight for the AUTO to register no flash. Sometimes if the cats are half asleep, I just get mean and get this flexible lamp to point in their face like this:
lamp
That close-up of her face turned out great!
And holy cow those cats look like real sisters!! She is sooooo pretty