this will be no easier for her..... @ 1.8 manual focusing a nifty fifty on moving kitties is pretty much as fun a sticking a fork in your eyeball...
For real, and she/he MIGHT get an eyeball in focus...or a pupil.
Cnh,
I don't know that I'm qualified to help you, really, since I'm pretty new myself.
But I know with my camera, I messed with (and STILL mess with) all the settings and modes, until I get something I'm happy with. Once I get something I'm happy, or semi-happy with, I try to work on how I can improve it.
The thing is, you CAN take pics of your cats without their eyes shutting, but that's going to require lessons in getting your camera settings just right, and that is going to require that you learn about aperture, shutter speed, and when and when NOT to mess with the ISO. And all that stuff can be overwhelming. But you'll be amazed at the shots you can get with your D60, once you've learned how to set the settings. You're going to want to mess with the settings and snap away. Just remember what you've set your camera at, so that when you get it right in certain lighting, then you'll remember what you had it set at for future reference.
I have a D60, too. I snapped this shot of my dog the other day with my 50mm lens, manual mode, f2.2 (I believe), 1/100 (photobucket is a LIAR), ISO 800.
She moves just as well and is unpredictable. ESPECIALLY when I've got a toy, bribing her to sit still. Sure, her nose is out of focus (because of my aperture), as well as her ears, but her eyes are damn sharp.
Your cats are white? Well, as you can see, my dog is black. I KNOW how hard it is to get a good picture of an animal. I most likely have the opposite problem you'll run into. Your cats will look washed out due to being white, while my dog looks underexposed ALL THE TIME.
Mess with your camera settings, find good lighting in your house, and just keep snapping. Oh, and be patient. I am.